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Paper Citation Record · LEDGER

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

As of 8 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 5 inbound Pith citation observations for arXiv:2506.02948.

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measured 59 of 59 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-02T00:54:50.434513Z

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Source: arxiv_reference, observed 2026-07-02T20:17:22.330990Z

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59 of 59 outbound references displayed

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Outbound references

Observation bf65f8eb-66ad-468d-8ca8-218e4be0a0fb · outbound

This paper cites Studies of the nonlinear problems I.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Studies of the nonlinear problems I

Reference 1

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Observation 2e67d76e-e520-423d-b81f-c3d29e220786 · outbound

This paper cites Exact discrete res- onances in the Fermi-Pasta-Ulam–Tsingou system.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Exact discrete res- onances in the Fermi-Pasta-Ulam–Tsingou system

Reference 2

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Observation 2ced9728-e0e0-46f7-9164-fb490cd2d1da · outbound

This paper cites Dimostrazione che in generale un sistema meccanico normale È QUASI—ergodico.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Dimostrazione che in generale un sistema meccanico normale È QUASI—ergodico

Reference 3

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Observation 585fb311-4fe4-433e-8796-04b7c63f001b · outbound

This paper cites Collected Papers:(Note E Memorie).

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Collected Papers:(Note E Memorie)

Reference 4

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Observation 322e4a6c-1d5d-43cf-90f1-f6f5bbf3d8e6 · outbound

This paper cites Counter-propagating waves on fluid surfaces and the contin- uum limit of the Fermi-Pasta-Ulam model.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Counter-propagating waves on fluid surfaces and the contin- uum limit of the Fermi-Pasta-Ulam model

Reference 5

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Observation ae08048e-8a13-4e84-8f10-4a88869ecc88 · outbound

This paper cites Interaction of.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Interaction of

Reference 6

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Observation 3f112ebe-fc0f-4759-855a-d58f9d8c79ad · outbound

This paper cites Statistical Properties of a Nonlinear String.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Statistical Properties of a Nonlinear String

Reference 7

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Observation 9f79660b-bea7-4748-913f-fc321ad4839c · outbound

This paper cites Stochastic instability of non-linear oscillations.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stochastic instability of non-linear oscillations

Reference 8

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Observation a798781c-a7c5-4713-b8a2-803a9c2adc83 · outbound

This paper cites The Fermi-Pasta-Ulam problem: a status report.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The Fermi-Pasta-Ulam problem: a status report

Reference 9

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Observation 009f1dbc-7f6b-4e2c-817f-7f590f645479 · outbound

This paper cites ProofofNishida’sconjectureonanharmoniclattices.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System ProofofNishida’sconjectureonanharmoniclattices

Reference 10

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Observation 70e65d7e-5ecb-4ed5-82cd-b254bc2c5d33 · outbound

This paper cites Results on normal forms for FPU chains.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Results on normal forms for FPU chains

Reference 11

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Observation 0c539df9-4cfd-4254-8cf1-268ef9731a53 · outbound

This paper cites Route to thermalization in the α-Fermi–Pasta–Ulam system.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Route to thermalization in the α-Fermi–Pasta–Ulam system

Reference 12

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Observation e271760b-4647-46ad-8a6e-a22f7c948c20 · outbound

This paper cites The two-stage dynamics in the Fermi-Pasta- Ulam problem: From regular to diffusive behavior.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The two-stage dynamics in the Fermi-Pasta- Ulam problem: From regular to diffusive behavior

Reference 13

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This paper cites The Fermi-Pasta-Ulam problem in the thermodynamic limit: Scaling laws of the energy cascade.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The Fermi-Pasta-Ulam problem in the thermodynamic limit: Scaling laws of the energy cascade

Reference 14

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Observation 6f2002b3-3044-4c6f-b075-991ca63f7f91 · outbound

This paper cites Anharmonic Chain with Lennard-Jones Interac- tion.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anharmonic Chain with Lennard-Jones Interac- tion

Reference 15

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Observation 6ee9281b-c38e-458b-aa65-423287d9d540 · outbound

This paper cites On the specific heat of Fermi–Pasta–Ulam systems and their glassy behavior.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the specific heat of Fermi–Pasta–Ulam systems and their glassy behavior

Reference 16

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Observation 52ad7994-18f8-4aba-8554-f872b5ba997e · outbound

This paper cites On the definition of temperature in FPU systems.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the definition of temperature in FPU systems

Reference 17

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Observation f5c90254-5304-415d-9f99-d0aa71c6a45a · outbound

This paper cites Localization of energy in FPU chains.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Localization of energy in FPU chains

Reference 18

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Observation dee12423-b9c1-4c0f-aab8-e3d6d937e42a · outbound

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On metastability in FPU

Reference 19

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System An averaging theorem for Hamiltonian dynamical systems in the thermodynamic limit

Reference 20

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This paper cites Some analytic results on the FPU paradox.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Some analytic results on the FPU paradox

Reference 21

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Observation e5047c16-b934-40e6-9ff6-9dd3143f83bf · outbound

This paper cites Zur kinetischen Theorie der Wärmeleitung in Kristallen.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Zur kinetischen Theorie der Wärmeleitung in Kristallen

Reference 22

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Observation 6a93647c-91f2-46c3-8cdc-6e8baa2f6b74 · outbound

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Theory of a weakly turbulent plasma

Reference 23

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This paper cites On the non-linear energy transfer in a gravity-wave spectrum. I. General theory.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the non-linear energy transfer in a gravity-wave spectrum. I. General theory

Reference 24

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the non-linear energy transfer in a gravity wave spectrum. II. Conservation the- orems; wave-particle analogy; irreversibility

Reference 25

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Zakharov, Victor S

Reference 26

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Observation d8ba893e-94f2-46e5-86cf-c7beab5cd95e · outbound

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Weak turbulence in media with a decay spectrum

Reference 27

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Nazarenko

Reference 28

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This paper cites The weakly nonlinear large-box limit of the 2D cu- bic nonlinear Schrödinger equation.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The weakly nonlinear large-box limit of the 2D cu- bic nonlinear Schrödinger equation

Reference 29

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Analysis of (CR) in higher dimension

Reference 30

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This paper cites Effective dynamics of the nonlinear Schrödinger equation on large domains.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Effective dynamics of the nonlinear Schrödinger equation on large domains

Reference 31

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This paper cites Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation

Reference 32

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This paper cites On the Boltzmann equation for weakly nonlinear wave equations.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the Boltzmann equation for weakly nonlinear wave equations

Reference 33

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation

Reference 34

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Observation fa4c5948-c1a3-49de-bc65-5c5e3fa9f6c8 · outbound

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Quantum diffusion of the random Schrödinger evolution in the scaling limit

Reference 35

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This paper cites On the derivation of the wave kinetic equation for NLS.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the derivation of the wave kinetic equation for NLS

Reference 36

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Observation 0e0bc2e1-1435-492f-90d3-b12fae1b3624 · outbound

This paper cites On the derivation of the homogeneous kinetic wave equation.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the derivation of the homogeneous kinetic wave equation

Reference 37

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Observation 1f546b0d-d157-43d3-91be-6231c6cae5ae · outbound

This paper cites Derivation of the homogeneous kinetic wave equation: longer time scales.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Derivation of the homogeneous kinetic wave equation: longer time scales

Reference 38

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Observation 2db5ec68-3f1e-42db-94f9-1fa30d3f3a27 · outbound

This paper cites Full derivation of the wave kinetic equation.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Full derivation of the wave kinetic equation

Reference 39

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Observation 7d323c57-2135-4d33-83a8-5b13fa0bc3ea · outbound

This paper cites Derivation of the wave kinetic equation: full range of scaling laws.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Derivation of the wave kinetic equation: full range of scaling laws

Reference 40

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Observation 99429a13-d76f-459e-a9d0-669d0a979828 · outbound

This paper cites Long time justification of wave turbulence theory.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Long time justification of wave turbulence theory

Reference 41

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source=pdf_text observed=2026-08-07T11:22:21.890705Z digest=sha256:da5dae6f1e2780adb8fb84d45209db3091c2080b6318d04c0329b1db6b709954

Observation 1adc147a-e9cf-4b72-b448-f19ccaa54918 · outbound

This paper cites Long time derivation of the Boltzmann equation from hard sphere dynamics.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Long time derivation of the Boltzmann equation from hard sphere dynamics

Reference 42

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source=pdf_text observed=2026-08-07T11:22:21.981271Z digest=sha256:6c03b736cb3b4f1000b02318dbe47b557da4d1e023c7ce28f6c93e137ec928a8

Observation 84eeb605-61c6-4867-9999-ddba60a1b9fd · outbound

This paper cites One-dimensional wave kinetic theory.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System One-dimensional wave kinetic theory

Reference 43

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Observation a5b34684-fd28-4b1b-8e73-c378e86d5e86 · outbound

This paper cites Stages of Energy Transfer in the FPU Model.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stages of Energy Transfer in the FPU Model

Reference 44

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source=pdf_text observed=2026-08-07T11:22:22.144733Z digest=sha256:a4a72c1c1a5bc17a716ddbebf28a7c8c5fba28c7d662a196e924f037c1b65443

Observation a930888d-0616-4678-8539-a1d8fb56cb69 · outbound

This paper cites Application of weak turbulence theory to FPU model.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Application of weak turbulence theory to FPU model

Reference 45

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source=pdf_text observed=2026-08-07T11:22:22.259616Z digest=sha256:e1bb8466daa0c94a22ce8f554017c5dcd4811478562ea8cbd32eb7e191269ad3

Observation 1d191f37-d020-4069-a815-12c357f94c2c · outbound

This paper cites Universal route to thermalization in weakly-nonlinear one-dimensional chains.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Universal route to thermalization in weakly-nonlinear one-dimensional chains

Reference 46

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source=pdf_text observed=2026-08-07T11:22:22.353098Z digest=sha256:f9ec0dce08227592b7c093f4941955ec0fd5f7607e7cf69526fdbcba32d1fb76

Observation d93094ff-8899-4be0-b7a8-b685ddc5802b · outbound

This paper cites Double scaling in the relaxation time in theβ-Fermi-Pasta-Ulam- Tsingou model.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Double scaling in the relaxation time in theβ-Fermi-Pasta-Ulam- Tsingou model

Reference 47

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source=pdf_text observed=2026-08-07T11:22:22.426466Z digest=sha256:4b4694a7c5f1cfb59ff17b2b3c663f8397e331fb625dd548a05a221251263ef4

Observation 800a4f6b-3677-484a-8c57-ff3065f3460a · outbound

This paper cites Coexistence of Ballistic and Fourier Regimes in theβ Fermi-Pasta-Ulam-Tsingou Lattice.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Coexistence of Ballistic and Fourier Regimes in theβ Fermi-Pasta-Ulam-Tsingou Lattice

Reference 48

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source=pdf_text observed=2026-08-07T11:22:22.495268Z digest=sha256:c787c1e23dfcaa98851f61f76d8cde89e7dae5d0e1a308b2e9a46d36dd388c1e

Observation e2a4c028-763a-43d6-8585-98a6e810f014 · outbound

This paper cites Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach

Reference 49

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source=pdf_text observed=2026-08-07T11:22:22.563947Z digest=sha256:e1ad8e3849e52e37c88d96abd1f3a45b1d015dc3d7b05e7b0899be229ba12b55

Observation 0883392f-f9e5-4da4-adff-d7e840f4b528 · outbound

This paper cites Anomalous energy transport in the FPU-β chain.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anomalous energy transport in the FPU-β chain

Reference 50

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source=pdf_text observed=2026-08-07T11:22:22.630552Z digest=sha256:80986a41615fc1c379b76185d59e0fd4830a6b8a3db8d0aee2508e53463a82df

Observation 4ef57354-c20e-4c6b-ad51-059ccdbc6909 · outbound

This paper cites Multi-wave resonances in the diatomic α-FPUT system.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Multi-wave resonances in the diatomic α-FPUT system

Reference 51

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source=pdf_text observed=2026-08-07T11:22:22.710436Z digest=sha256:3b463e7136249658f4c2f232269316c3791a5ccee3ac1d2b8cee119e93d4f55e

Observation 7fcf360c-16f2-4e10-bb13-42728e42b746 · outbound

This paper cites Quasiperiodicity in the α-Fermi–Pasta–Ulam–Tsingou problem revisited: An ap- proach using ideas from wave turbulence.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Quasiperiodicity in the α-Fermi–Pasta–Ulam–Tsingou problem revisited: An ap- proach using ideas from wave turbulence

Reference 52

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source=pdf_text observed=2026-08-07T11:22:22.787102Z digest=sha256:890d41f5eb1d5c69dc374e6370aefebdcd42a377864aba74462a52189da289ea

Observation 71ae2a53-33f4-4416-a557-662db14f86e8 · outbound

This paper cites Six-wave systems in one-dimensional wave turbulence.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Six-wave systems in one-dimensional wave turbulence

Reference 53

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source=pdf_text observed=2026-08-07T11:22:22.864727Z digest=sha256:a3e61b60d9a412b242b535a54381c4f8721c0e17d4dcfa0a9a9d1a98c24ee9c6

Observation 1343b459-0aa3-4247-b1ac-e5754bc53f8c · outbound

This paper cites 4-wave dynamics in kinetic wave tur- bulence.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System 4-wave dynamics in kinetic wave tur- bulence

Reference 54

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source=pdf_text observed=2026-08-07T11:22:22.941562Z digest=sha256:bf84388069a1d13af61fc20ac540b8934e085a8a27fa287003e586f7e282f477

Observation c968a359-9e77-4a76-acfd-d6f2e9d333ef · outbound

This paper cites On the wave turbulence theory of 2D gravity waves, II: propagation of randomness.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the wave turbulence theory of 2D gravity waves, II: propagation of randomness

Reference 55

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source=pdf_text observed=2026-08-07T11:22:23.007115Z digest=sha256:b8cf5386e1061678b6924114c42218e9d6b4430d81f4d6c456df386cf6a979c4

Observation b4f0193e-ae6a-4820-accf-28efbba9392d · outbound

This paper cites A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations

Reference 56

Resolution
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 1f5b4aa5-1ede-48f1-88b4-0fb4835f5019 · outbound

This paper cites an unresolved cited work.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Unresolved cited work

Reference 276

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source=pdf_text observed=2026-08-07T11:22:20.454921Z digest=sha256:616e9bc6d0b8e082a0863af7aa21b20ab3caa907a95a45f2c845e7dbe71dd26d

Observation a9963eb2-5bf7-42e2-83ee-435dfc051f07 · outbound

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Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Unresolved cited work

Reference 312

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source=pdf_text observed=2026-08-07T11:22:21.400293Z digest=sha256:286c9034a1d94fc10df90d50e5cf8129f375823e11e16023f08b67151d77bb57

Observation 7c778b1e-161f-4903-9c47-ac9dd6eb396b · outbound

This paper cites Stages of Energy Transfer in the FPU Model.

Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stages of Energy Transfer in the FPU Model

Reference 2002

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source=pdf_text observed=2026-08-07T11:22:22.208481Z digest=sha256:cea43a02dfb16db4a17c6947826f6062d1145e0024eee495f4ebe56be6a52590

Pith citing papers

Observation a6fd4837-06ca-4618-86a6-1a50690fbf69 · inbound

Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System cites this paper.

Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

Reference 76

Resolution
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arxiv_id, observed 2026-05-20T04:48:06.030521Z

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Observation 4a2e226a-b5d9-4fdd-8478-3d819e26ef7c · inbound

Resonant interactions in the $\alpha$-FPUT lattice with site-dependent coefficients cites this paper.

Resonant interactions in the $\alpha$-FPUT lattice with site-dependent coefficients Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

Reference 31

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arxiv_id, observed 2026-06-30T14:24:45.279382Z

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Observation 3c54c731-096f-47ad-bb55-7d3af9455daf · inbound

A review on the kinetic theory of oscillator chains cites this paper.

A review on the kinetic theory of oscillator chains Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

Reference 13

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arxiv_id, observed 2026-07-01T21:56:15.110246Z

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source=pdf_text observed=2026-06-28T16:13:24.537123Z digest=sha256:b8f1b25e7ad2bc583862c1ae83181f0e92cbd869c011c9eb5bbf6243f20481d7

Observation 43b9389a-94f9-479f-828e-840618cd3541 · inbound

A survey on rigorous results for the dynamics of periodic FPU chains cites this paper.

A survey on rigorous results for the dynamics of periodic FPU chains Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

Reference 38

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arxiv_id, observed 2026-07-02T20:17:22.332828Z

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source=pdf_text observed=2026-06-27T20:36:36.543636Z digest=sha256:0ef66dcfc135ee9fffd1e3ccc52cf4915bf8ee518ef0479a92b6a7e6fda751d8

Observation 4c4acca1-d77d-45a2-83ec-5453b9835009 · inbound

Sharp decay thresholds in weighted $L^\infty$ for wave kinetic equations with power-law dispersion cites this paper.

Sharp decay thresholds in weighted $L^\infty$ for wave kinetic equations with power-law dispersion Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System

Reference 30

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no resolver link, observed 2026-08-02T00:54:50.434513Z

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source=pdf_text observed=2026-08-02T00:54:50.434513Z digest=sha256:50d27bd5c04ad85a5b34fa74ac8c5c795af676c9b1e50f4d8016e812ce185907