Paper Citation Record · LEDGER

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions

As of 23 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2412.08064.

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

pith.paper-citation-record.v1
2412.08064 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:22:03.064081Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:49:09.800001Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T18:49:10.401026Z

Reference resolution

14 of 14 outbound references displayed

verified exact0
verified fuzzy9
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 842cd002-f114-4f79-a8d7-eca78ef59d2d · outbound

This paper cites an unresolved cited work.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:22:03.519110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9618691b-952f-4d73-b1ee-ba2ec1a47edb · outbound

This paper cites In these two cases, the coordinates of the random vectors are independently distributed according to either the standard normal distribution or the t(6) distribution.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions In these two cases, the coordinates of the random vectors are independently distributed according to either the standard normal distribution or the t(6) distribution

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.489730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 882fd795-20ba-4f52-8e30-983bd8efcb55 · outbound

This paper cites With some abuse of notation, denote ∇φ0(z) = F(z).

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions With some abuse of notation, denote ∇φ0(z) = F(z)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.467310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6ec5567c-6470-4e5e-a38d-eb071399d31d · outbound

This paper cites an unresolved cited work.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:22:03.440859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 85f39f16-bf5e-4c88-89cc-8bf1bd2c9693 · outbound

This paper cites For the multivariate case, where the OT maps are functions between two Rd spaces, we define the OT maps to be the composition of these three cases: for z = (z1, · · ·, zd)⊤ ∈ Rd,.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions For the multivariate case, where the OT maps are functions between two Rd spaces, we define the OT maps to be the composition of these three cases: for z = (z1, · · ·, zd)⊤ ∈ Rd,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.409230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2d9e6953-c3f8-4db6-a1bc-815ebab35078 · outbound

This paper cites F(zd)  .

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions F(zd)  

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.372801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2cbc2cef-ad3e-4de6-8527-cf43626b8629 · outbound

This paper cites 3zd + 5  .

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions 3zd + 5  

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.342502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c2687496-8fbc-42a3-b3cc-f59123e10f33 · outbound

This paper cites sign(zd) · z2 d  .

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions sign(zd) · z2 d  

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.315844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9af12e2a-24bf-46ec-9fe7-42f376dcb3aa · outbound

This paper cites an unresolved cited work.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:22:03.278008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0fc133c5-c992-4d9b-8304-83d172820295 · outbound

This paper cites curse of dimensionality.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions curse of dimensionality

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.247034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a39c4b92-3def-44a7-a621-499751c4775e · outbound

This paper cites This discrepancy is particularly pronounced when estimating the signed-quadratic OT map, which has a larger b parameter in terms 35 of (β, b)-smoothness.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions This discrepancy is particularly pronounced when estimating the signed-quadratic OT map, which has a larger b parameter in terms 35 of (β, b)-smoothness

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.225100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 825bf046-bcb0-4074-88fb-fd611257b5b6 · outbound

This paper cites an unresolved cited work.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:22:03.201539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation faf146de-290b-491d-9bd4-66a932f0eb9b · outbound

This paper cites an unresolved cited work.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:22:03.175322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 543f9231-cccf-45e8-95d0-1bd7f839c05d · outbound

This paper cites In the outer regions, where P has a smaller probability mass, the OT map estimators tend to perform poorly.

Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions In the outer regions, where P has a smaller probability mass, the OT map estimators tend to perform poorly

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:22:03.135203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 198cf994-f02a-4507-a83b-2b673c12fc33 · inbound

Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives cites this paper.

Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:49:10.405178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.