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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2506.02948 v2

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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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Observation 60058322-f00c-4b32-a458-cc0cdc4d6892 · outbound

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

This paper cites On metastability in FPU.

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

Reference 19

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Observation 6890c7d6-52e2-4dde-bba6-16bbd34012e8 · outbound

This paper cites An averaging theorem for Hamiltonian dynamical systems in the thermodynamic limit.

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

This paper cites Theory of a weakly turbulent plasma.

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

Reference 23

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Observation 1e7176a3-906d-4dd6-b758-f172d5a26e0d · outbound

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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This paper cites On the non-linear energy transfer in a gravity wave spectrum. II. Conservation the- orems; wave-particle analogy; irreversibility.

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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This paper cites Zakharov, Victor S.

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

Reference 26

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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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Observation 26fa3725-3fe4-4688-b1b1-456973443f32 · outbound

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

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

Reference 39

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

Reference 41

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

Reference 43

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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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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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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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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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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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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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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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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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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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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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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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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

Resolution: unresolved; no resolver link, observed 2026-08-07T11:22:23.007115Z

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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: verified exact; doi, observed 2026-08-07T11:22:23.235527Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-07T11:22:20.454921Z

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

This paper cites an unresolved cited work.

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

Reference 312

Resolution: unresolved; no resolver link, observed 2026-08-07T11:22:21.400293Z

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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

Resolution: unresolved; no resolver link, observed 2026-08-07T11:22:22.208481Z

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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: verified exact; arxiv_id, observed 2026-05-20T04:48:06.030521Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T14:24:45.279382Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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

Resolution: verified exact; arxiv_id, observed 2026-07-01T21:56:15.110246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:17:22.332828Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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

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

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