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Paper Citation Record · LEDGER

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs

As of 16 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 1 inbound Pith citation observation for arXiv:2412.13672.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.13672 v2

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T13:02:48.077092Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T00:10:16.742500Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-03T21:48:59.694434Z

Reference resolution

48 of 48 outbound references displayed

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  • verified fuzzy39
  • unresolved5
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External citation measurements

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Outbound references

Observation 6b85f048-6d32-4ffd-a312-eb0e0117c7a0 · outbound

This paper cites Aldous, Brownian excursions, critical random graphs and the multip licative coalescent , The Annals of Probability (1997), 812–854.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Aldous, Brownian excursions, critical random graphs and the multip licative coalescent , The Annals of Probability (1997), 812–854

Reference 1

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation d44a2983-d95b-416d-b986-be82eecbca90 · outbound

This paper cites J Aldous, Deterministic and stochastic models for coalescence (aggr egation and coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1999), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs J Aldous, Deterministic and stochastic models for coalescence (aggr egation and coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1999), no

Reference 2

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Observation c847e0d9-b867-4e06-962e-af74edbe4d1f · outbound

This paper cites Andreis, W.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Andreis, W

Reference 3

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Observation 5815f71c-b096-479c-b728-585a99694369 · outbound

This paper cites B Athreya and P.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs B Athreya and P

Reference 4

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Observation da5df5e8-ce49-4a48-ba07-00272ea91883 · outbound

This paper cites Ball and P.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Ball and P

Reference 5

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Observation 010b8256-17d6-475f-90c1-9d202776d7c0 · outbound

This paper cites Barbour and A.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Barbour and A

Reference 6

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Observation 32a27252-0656-42ba-8e28-ae127e1b66c6 · outbound

This paper cites We begi n with the following lemma.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs We begi n with the following lemma

Reference 7

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Observation 360af0c7-cf9e-4887-924d-41a14461242e · outbound

This paper cites k-th level truncation.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs k-th level truncation

Reference 8

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source=pdf_text observed=2026-08-11T13:02:47.753394Z digest=sha256:5c6e4a2d118c323eee3020f0ab3d73c1d71785802b68f092ce05d75a5d2dda63

Observation 75818a16-1e69-4c3e-b856-fb0565c876e5 · outbound

This paper cites Scaling limits and universality: Critical percolation on weighted graphs converging to an $L^3$ graphon.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Scaling limits and universality: Critical percolation on weighted graphs converging to an $L^3$ graphon

Reference 9

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Observation 88a8572d-7519-4f8c-a60f-453fc9fa4aa0 · outbound

This paper cites Bhamidi, A.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bhamidi, A

Reference 10

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Observation cf27e69c-b31c-43a2-a2b9-2d9d8fb6e53a · outbound

This paper cites Bhamidi, A.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bhamidi, A

Reference 11

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Observation 8b2b8f1a-37b4-469e-91ec-796c0b80bf11 · outbound

This paper cites Bhamidi, A.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bhamidi, A

Reference 12

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Observation bf9580f2-e70d-437d-a24b-cfcdaea22655 · outbound

This paper cites Bollob ´as, Random Graphs, Second, Cambridge Studies in Advanced Mathematics, vol.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bollob ´as, Random Graphs, Second, Cambridge Studies in Advanced Mathematics, vol

Reference 13

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Observation 6f2741e5-8172-49c5-bd4b-005cc4101db7 · outbound

This paper cites Bollob ´as, C.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bollob ´as, C

Reference 14

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Observation 266aaebc-a9a9-4eb3-aeae-e5102c3811ed · outbound

This paper cites Bollob ´as, S.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bollob ´as, S

Reference 15

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Observation f0313e71-b012-4dd0-b9d9-e45eb996ba47 · outbound

This paper cites Bollob ´as and O.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Bollob ´as and O

Reference 16

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Observation 0db0dde0-3241-4c37-b897-296d9ac84440 · outbound

This paper cites A central limit theorem for the giant in a stochastic block model.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs A central limit theorem for the giant in a stochastic block model

Reference 17

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Observation 4f88d03f-ded0-4369-bbb3-c585ed9b9cf3 · outbound

This paper cites A novel approach to the giant component fluctuations.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs A novel approach to the giant component fluctuations

Reference 18

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:02:47.878344Z digest=sha256:01375f1b52afc9ec0bb1a19114026e184693f5ddd4f028ae4adfbeda137cebdf

Observation baaa630c-7402-4d45-a02f-353ae0c83dd2 · outbound

This paper cites Corujo, The number of connected components in sub-critical random g raph processes, 2024.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Corujo, The number of connected components in sub-critical random g raph processes, 2024

Reference 19

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source=pdf_text observed=2026-08-11T13:02:47.884477Z digest=sha256:4dab9be80ab9a9395b4c3d735aba6be548ffd8ce27752cc6894126ccaed2661d

Observation 17b31bc0-0566-474f-881d-f319df2b8ba7 · outbound

This paper cites Da Prato and J.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Da Prato and J

Reference 20

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Observation 8fd8c5c9-9fc4-4b38-931d-14b4db83c62f · outbound

This paper cites Durrett, Random graph dynamics , Cambridge Series in Statistical and Probabilistic Mathem atics, vol.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Durrett, Random graph dynamics , Cambridge Series in Statistical and Probabilistic Mathem atics, vol

Reference 21

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source=pdf_text observed=2026-08-11T13:02:47.898921Z digest=sha256:82cb7cc708dbc6f414bcba69aaa24e74788e66a3ec9b1bc8f8200d021907fa91

Observation 538e5e02-891b-4f81-b719-dae27aebb484 · outbound

This paper cites Enriquez, G.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Enriquez, G

Reference 22

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Observation 29304086-5b93-43f9-bcaf-77849a5ae211 · outbound

This paper cites Erdos, A.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Erdos, A

Reference 23

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source=pdf_text observed=2026-08-11T13:02:47.913030Z digest=sha256:6857b4ba0125e6ba7aec8979022d7f0eb18f76e0c42eb9c4ed9b85f8722df759

Observation 33647e12-9b35-4fc9-9302-87bc9c721fa0 · outbound

This paper cites Ethier and T.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Ethier and T

Reference 24

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source=pdf_text observed=2026-08-11T13:02:47.919916Z digest=sha256:0fca724491b7ec24978ef2953d94bfa71373a9de9b74c1e8a29fb5d0275df51c

Observation ba684dcf-ee55-406e-aa1a-a93308113ae4 · outbound

This paper cites M Frieze, On the value of a random minimum spanning tree problem , Discrete Applied Mathematics 10 (1985), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs M Frieze, On the value of a random minimum spanning tree problem , Discrete Applied Mathematics 10 (1985), no

Reference 25

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source=pdf_text observed=2026-08-11T13:02:47.926379Z digest=sha256:52be607dd16475b15d9005cea0578dfe68db35cd19231ae5e531a8c29b51b4c3

Observation 78f12278-d97d-42c2-ab5f-e34e57ae276e · outbound

This paper cites Random minimum spanning tree and dense graph limits.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Random minimum spanning tree and dense graph limits

Reference 26

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source=pdf_text observed=2026-08-11T13:02:47.932562Z digest=sha256:44a599117b1c9e8fdb82ca7de90d1d58facc4dde52e31f9cbc57c188389d0e69

Observation b351dad1-0854-4c76-a72a-aa8919169be2 · outbound

This paper cites Janson, The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph, Random Structures & Algorithms 7 (1995), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Janson, The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph, Random Structures & Algorithms 7 (1995), no

Reference 27

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source=pdf_text observed=2026-08-11T13:02:47.938066Z digest=sha256:a13f16c5a850415a31201f74914475e730d883ad40a9566076c4ea9951410def

Observation 5f1fd6fa-6e86-470c-8ed8-be965663127a · outbound

This paper cites Janson, Asymptotic equivalence and contiguity of some random graph s, Random Structures & Algorithms 36 (2010), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Janson, Asymptotic equivalence and contiguity of some random graph s, Random Structures & Algorithms 36 (2010), no

Reference 28

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Observation 2372ff1b-0721-46ae-a801-b7c437e2ee52 · outbound

This paper cites Janson, T.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Janson, T

Reference 29

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Observation a29dcc57-d66d-458f-a165-9e1f64b04ef8 · outbound

This paper cites an unresolved cited work.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Unresolved cited work

Reference 30

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Observation f9794bcc-a39b-4b3f-91f6-96440bb196eb · outbound

This paper cites Karatzas and S.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Karatzas and S

Reference 31

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Observation 674f397b-bad9-48fd-aa40-fdf96175c055 · outbound

This paper cites an unresolved cited work.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Unresolved cited work

Reference 32

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source=pdf_text observed=2026-08-11T13:02:47.969173Z digest=sha256:637627a5ac7a212886918be027bff9722b96f225f7bef772aeee929157a09214

Observation ac967385-a9fd-4405-8e4f-61fd7d950da2 · outbound

This paper cites Kovchegov and P.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Kovchegov and P

Reference 33

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source=pdf_text observed=2026-08-11T13:02:47.973738Z digest=sha256:7b0b41324b3095d9a2173beb39c9c5f5a016d597abee2ae8172145940421d330

Observation fe5c7e51-c939-4f4f-98bd-ce5f5974c72f · outbound

This paper cites G Kurtz, Approximation of Population Processes, SIAM, 1981.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs G Kurtz, Approximation of Population Processes, SIAM, 1981

Reference 34

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source=pdf_text observed=2026-08-11T13:02:47.978654Z digest=sha256:66f74cdd1e715e391b81ec9d65102f7cddc3b7331eabc5e01fac29d2e90e44f7

Observation 86e15660-a6f2-46a6-a960-7ce91b89e2c4 · outbound

This paper cites Limic, The eternal multiplicative coalescent encoding via excursions of L ´evy-type processes, Bernoulli 25 (2019), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Limic, The eternal multiplicative coalescent encoding via excursions of L ´evy-type processes, Bernoulli 25 (2019), no

Reference 35

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:47.985411Z digest=sha256:e46fcfa1678c6f2d29f84b1cc4d6bcd50779124bf16354b0da99833a2e459c2a

Observation 9c492362-8075-472a-bf2f-41d7e898610e · outbound

This paper cites Lov ´asz, Large Networks and Graph Limits, American Mathematical Society Colloquium Publications, vol.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Lov ´asz, Large Networks and Graph Limits, American Mathematical Society Colloquium Publications, vol

Reference 36

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source=pdf_text observed=2026-08-11T13:02:47.991991Z digest=sha256:b1438ad4fcdec0ae27e04b7ec5338b96a52905212151bb1fd68d5746da869a0d

Observation c5d3a6c0-ed70-4baa-a007-06dc24340187 · outbound

This paper cites Molloy and B.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Molloy and B

Reference 37

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source=pdf_text observed=2026-08-11T13:02:47.998050Z digest=sha256:8f40c626f8dc11700fee204e5180005b567f27aeca02a3e5a091189a722a6d52

Observation aca587d1-7127-427c-8988-6840e6e58b41 · outbound

This paper cites R Norris, Smoluchowski’s coagulation equation: uniqueness, nonuni queness and a hydrodynamic limit for the stochastic coalescent, The Annals of Applied Probability 9 (1999), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs R Norris, Smoluchowski’s coagulation equation: uniqueness, nonuni queness and a hydrodynamic limit for the stochastic coalescent, The Annals of Applied Probability 9 (1999), no

Reference 38

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raw_fallback, observed 2026-08-11T13:02:48.657710Z

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source=pdf_text observed=2026-08-11T13:02:48.010144Z digest=sha256:693e371d88b08da2197f866cea48883ed51c3c0855418ab165bc9a5c3e14a8fc

Observation 6e087f03-2698-4199-a168-08a843043404 · outbound

This paper cites Pittel, On tree census and the giant component in sparse random graph s, Random Structures & Algorithms 1 (1990), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Pittel, On tree census and the giant component in sparse random graph s, Random Structures & Algorithms 1 (1990), no

Reference 39

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raw_fallback, observed 2026-08-11T13:02:48.638133Z

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source=pdf_text observed=2026-08-11T13:02:48.019143Z digest=sha256:c504079044495806d53937a062be76ea8740992321da14656b9d8191c87f6737

Observation 9d0c141e-ffb4-40fa-b2d8-941b43a7a7ef · outbound

This paper cites Pittel and N.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Pittel and N

Reference 40

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verified fuzzy
raw_fallback, observed 2026-08-11T13:02:48.619570Z

Source-reported events for the cited work

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source=pdf_text observed=2026-08-11T13:02:48.026503Z digest=sha256:68aceecd8c871260fa1531e4e72a98b525912a083d907b1b7b633f3f5649c411

Observation 2f26cdc1-3810-4f8c-b5e5-f37c8b1c3298 · outbound

This paper cites an unresolved cited work.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Unresolved cited work

Reference 41

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unresolved
raw_fallback, observed 2026-08-11T13:02:48.602154Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.032191Z digest=sha256:e64252477a9dba7cb1fc1f0e9989448f59c7e78960a6f49dbb8ecbd42d002a19

Observation adc95b0c-71c9-411c-bd09-65f6c9b55f21 · outbound

This paper cites Riordan, The phase transition in the configuration model , Combinatorics, Probability and Computing 21 (2012), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Riordan, The phase transition in the configuration model , Combinatorics, Probability and Computing 21 (2012), no

Reference 42

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raw_fallback, observed 2026-08-11T13:02:48.578996Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.039194Z digest=sha256:7779bfbd2c37f5cecfbfec46a5ea93f988cb717536881a680e68227b5f78d653

Observation 90b13c48-be98-4bfc-9006-e524719d8377 · outbound

This paper cites an unresolved cited work.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Unresolved cited work

Reference 43

Resolution
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raw_fallback, observed 2026-08-11T13:02:48.557935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.044749Z digest=sha256:d4f7e72ecff6d1eb2e3910c72f3c20a878869db3bd95df7d42955511bea17c1a

Observation dbab3c05-f8c4-4967-9c85-1e93f09ac0a2 · outbound

This paper cites Spencer and N.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Spencer and N

Reference 44

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raw_fallback, observed 2026-08-11T13:02:48.530153Z

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source=pdf_text observed=2026-08-11T13:02:48.051521Z digest=sha256:f12b8a7aa68b50ce0a275caee877dd3ec3e4125b01bb7ef980db486a73860f85

Observation b59af0c6-b76a-4e8b-a06f-0b3a8d73b9b0 · outbound

This paper cites Steele, On Frieze’sχ (3) limit for lengths of minimal spanning trees, Discrete Applied Mathematics 18 (1987), no.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Steele, On Frieze’sχ (3) limit for lengths of minimal spanning trees, Discrete Applied Mathematics 18 (1987), no

Reference 45

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raw_fallback, observed 2026-08-11T13:02:48.496181Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.058188Z digest=sha256:745d89ff60ddd8656271cb5fec1cc1244e20703e3aa5fa5f08fdab4155c37152

Observation 9aaf9a39-dba3-428f-abcb-a4ad3fc1cdce · outbound

This paper cites van der Hofstad, Random Graphs and Complex Networks.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs van der Hofstad, Random Graphs and Complex Networks

Reference 46

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.066128Z digest=sha256:2598801c3bd056067e53528b77ebb69a190c8c024d459c44f0deb45a080a1a37

Observation 03a0eab2-5aa8-4d89-82a6-4d896e6e79ca · outbound

This paper cites van der Hofstad, Random Graphs and Complex Networks.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs van der Hofstad, Random Graphs and Complex Networks

Reference 47

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:02:48.071447Z digest=sha256:c10f18d9c4e7ae2f6e4c4150538f7dae1a1d55c705e050e51af73bc0e3b76ca6

Observation 75614366-ff85-445f-b73e-76a787e7b1cd · outbound

This paper cites Yu and W.

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs Yu and W

Reference 48

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no resolver link, observed 2026-08-11T13:02:48.077092Z

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source=pdf_text observed=2026-08-11T13:02:48.077092Z digest=sha256:6a3c505224733cc22abb469166a750a7f0c0181b43f37e45f112c9868f56545b

Pith citing papers

Observation 9a1a1f4a-fc81-4836-ba53-27068a334ead · inbound

Asymptotics of the number of labelled connected sparse multitype graphs cites this paper.

Asymptotics of the number of labelled connected sparse multitype graphs Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs

Reference 6

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source=pdf_text observed=2026-06-27T00:10:16.742500Z digest=sha256:69f5d501511ce38b55428d848f7dc9ed52c892b9ddb0dc5984269a71439e274c