Paper Citation Record · LEDGER

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus

As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2606.30223.

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2606.30223 v1

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Outbound references

Observation 9432b017-b603-4574-a887-993aa8a2d36d · outbound

This paper cites Periodic nonlinear Schr¨ odinger equation and invariant measures.Comm.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Periodic nonlinear Schr¨ odinger equation and invariant measures.Comm

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Observation bb574bc3-5b13-4d74-a761-50efc6f98544 · outbound

This paper cites Invariant measures for the 2d-defocusing nonlinear Schr¨ odinger equation.Comm.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant measures for the 2d-defocusing nonlinear Schr¨ odinger equation.Comm

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Observation 9b845a3d-4d23-4bcc-b0cb-913d767d431b · outbound

This paper cites Invariant measures for the Gross-Piatevskii equation.J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant measures for the Gross-Piatevskii equation.J

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Observation 57e2758f-a2f7-47f6-b04b-89af1b9fd83a · outbound

This paper cites Almost sure global well posedness for the radial nonlinear Schr¨ odinger equation on the unit ball I: the 2D case.Ann.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Almost sure global well posedness for the radial nonlinear Schr¨ odinger equation on the unit ball I: the 2D case.Ann

Reference 4

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Observation 843c468d-499a-4409-bdb6-49163789c6ef · outbound

This paper cites Almost sure global well-posedness for the radial nonlinear Schr¨ odinger equation on the unit ball II: the 3D case.J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Almost sure global well-posedness for the radial nonlinear Schr¨ odinger equation on the unit ball II: the 3D case.J

Reference 5

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Observation d5fbad32-5576-40b6-bd85-d2c412dcf6c0 · outbound

This paper cites Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball.J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball.J

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Observation 403b53d6-5c10-464e-ab87-d1a9e6fa662f · outbound

This paper cites Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: dynamics.J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: dynamics.J

Reference 7

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Observation 5ad150d3-9cf5-4d6b-8bbe-e7b2b5ad6a47 · outbound

This paper cites Wick powers in stochastic PDEs: an introduction.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Wick powers in stochastic PDEs: an introduction

Reference 8

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Observation 5b361181-66d9-403a-b6e2-d2ce725ed5bf · outbound

This paper cites On restricted-type Strichartz estimates and the applications.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus On restricted-type Strichartz estimates and the applications

Reference 9

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Observation 6a5ba811-dde5-44e9-977c-0d190c656003 · outbound

This paper cites Nahmod, and Haitian Yue.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Nahmod, and Haitian Yue

Reference 10

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Observation 75a71a1f-94d4-4aa4-9f16-664bd0937813 · outbound

This paper cites Nahmod, and Haitian Yue.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Nahmod, and Haitian Yue

Reference 11

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Observation 2ede3631-0301-4ee5-85e4-5902dc2d9065 · outbound

This paper cites Nahmod, and Haitian Yue.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Nahmod, and Haitian Yue

Reference 12

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Observation 37e6a5da-7f3c-4c40-9145-6756870a93a5 · outbound

This paper cites 2D-defocusing nonlinear Schr¨ odinger equation with random data on irrational tori.Stoch.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus 2D-defocusing nonlinear Schr¨ odinger equation with random data on irrational tori.Stoch

Reference 13

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Observation f5caf368-d1b2-440f-b0f5-e3b099c7e44a · outbound

This paper cites Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces, 2025.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces, 2025

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-06-30T14:44:45.764521Z

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Observation 63ebd51e-49e4-491e-892d-0b2976541d97 · outbound

This paper cites Springer-Verlag, New York, second edition, 1987.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Springer-Verlag, New York, second edition, 1987

Reference 15

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Observation b5dffc98-73af-4237-bcbb-c2baa32a1fd7 · outbound

This paper cites Paracontrolled distributions and singular PDEs.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Paracontrolled distributions and singular PDEs

Reference 16

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Observation 5209ae0b-d049-4f31-a2db-cdc66520e150 · outbound

This paper cites A Fourier analytic approach to pathwise sto- chastic integration.Electron.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus A Fourier analytic approach to pathwise sto- chastic integration.Electron

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Observation f28122c7-bcf8-4cf5-ae99-8583d4046183 · outbound

This paper cites Solving the KPZ equation.Ann.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Solving the KPZ equation.Ann

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Observation cf64bd96-bbdd-4114-b9ad-f587f12e2ac4 · outbound

This paper cites Singular stochastic PDEs.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Singular stochastic PDEs

Reference 19

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Observation 670e8262-00a8-4759-8373-b51d19493d0f · outbound

This paper cites IV, pages 49–73.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus IV, pages 49–73

Reference 20

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Observation ecabc2e3-9729-4250-8b16-219a855d42bc · outbound

This paper cites A theory of regularity structures.Invent.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus A theory of regularity structures.Invent

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Observation 9aca3c8c-6a12-4163-8bca-d8a5ca24eef2 · outbound

This paper cites Introduction to regularity structures.Braz.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Introduction to regularity structures.Braz

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Observation b45c3c3b-851a-41dd-9b04-8cec64d955b8 · outbound

This paper cites Bounding the number of lattice points near a convex curve by curvature.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Bounding the number of lattice points near a convex curve by curvature

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Observation e3a1d6ef-268b-4d1e-8117-090c17193033 · outbound

This paper cites On the continuum limit for discrete NLS with long- range lattice interactions.Comm.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus On the continuum limit for discrete NLS with long- range lattice interactions.Comm

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Observation 6932d4e1-fbe3-4480-af3e-fb38f095e8c4 · outbound

This paper cites Renormalization group and stochastic PDEs.Ann.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Renormalization group and stochastic PDEs.Ann

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Observation b53f334a-e05a-4d1b-ba95-4a32e029f36a · outbound

This paper cites World Scientific Publishing Co.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus World Scientific Publishing Co

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Observation 11d5f7b0-01a7-403b-968b-b28dcd2e80bf · outbound

This paper cites Fractional quantum mechanics and L´ evy path integrals.Phys.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Fractional quantum mechanics and L´ evy path integrals.Phys

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Observation bac2a7fb-2221-4d34-8569-9bce7d235183 · outbound

This paper cites Lebowitz, Harvey A.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Lebowitz, Harvey A

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Observation 0c305b30-6c86-4369-bb43-858f564af740 · outbound

This paper cites Gibbs measure for the focusing fractional NLS on the torus.SIAM J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Gibbs measure for the focusing fractional NLS on the torus.SIAM J

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Observation db6afb65-6e97-42ef-8dec-6de3c751caf9 · outbound

This paper cites Gibbs dynamics for fractional nonlinear Schr¨ odinger equations with weak disper- sion.Comm.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Gibbs dynamics for fractional nonlinear Schr¨ odinger equations with weak disper- sion.Comm

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Observation 80dea689-f913-47cc-ada7-b4a5c7a509fc · outbound

This paper cites Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic $\Phi^4_3$-model.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic $\Phi^4_3$-model

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Resolution: verified exact; arxiv_id, observed 2026-06-30T14:44:45.761862Z

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Observation 4e1029f6-8911-4e44-96b3-ce53f035d40e · outbound

This paper cites Optimal integrability threshold for Gibbs measures asso- ciated with focusing NLS on the torus.Invent.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Optimal integrability threshold for Gibbs measures asso- ciated with focusing NLS on the torus.Invent

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Observation 12511ef0-e7ae-45b3-8153-5c26691bac50 · outbound

This paper cites A pedestrian approach to the invariant Gibbs measures for the 2-ddefo- cusing nonlinear Schr¨ odinger equations.Stoch.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus A pedestrian approach to the invariant Gibbs measures for the 2-ddefo- cusing nonlinear Schr¨ odinger equations.Stoch

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Observation c04290b6-bdba-4896-b77e-889aead73903 · outbound

This paper cites Solving the 4NLS with white noise initial data.Forum Math.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Solving the 4NLS with white noise initial data.Forum Math

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Observation 051858f3-ac2a-4862-bda9-119cca93bcf5 · outbound

This paper cites Princeton Series in Physics.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Princeton Series in Physics

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Observation a71a125e-88cd-4f42-b04e-7de8ae3c8f99 · outbound

This paper cites Springer-Verlag, New York, 1999.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Springer-Verlag, New York, 1999

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Observation 001189ea-dc41-4164-864e-a381a8e6bf14 · outbound

This paper cites Gibbs measure dynamics for the fractional NLS.SIAM J.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Gibbs measure dynamics for the fractional NLS.SIAM J

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Observation b924bc6a-9d17-4304-a802-034e2bdf728d · outbound

This paper cites Refined probabilistic global well-posedness for the weakly dispersive NLS.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Refined probabilistic global well-posedness for the weakly dispersive NLS

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Observation 44438670-2f40-4a08-a840-3255bf6746a0 · outbound

This paper cites Weak universality results for a class of nonlinear wave equa- tions.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Weak universality results for a class of nonlinear wave equa- tions

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Observation 1b694eb8-0e5d-4467-ab97-74f800a59d59 · outbound

This paper cites Global well-posedness and long-time behavior of the fractional NLS.Stoch.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Global well-posedness and long-time behavior of the fractional NLS.Stoch

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Observation b320afd0-b209-4314-b871-205d5c031811 · outbound

This paper cites Invariant measures for the nonlinear Schr¨ odinger equation on the disc.Dyn.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant measures for the nonlinear Schr¨ odinger equation on the disc.Dyn

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Observation 879f8906-e05c-4665-b92e-750cdd960709 · outbound

This paper cites Invariant measures for the defocusing nonlinear Schr¨ odinger equation.Ann.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Invariant measures for the defocusing nonlinear Schr¨ odinger equation.Ann

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Observation aa130dcc-caa9-4068-95dd-79c65b8a2993 · outbound

This paper cites Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on ^ d.

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on ^ d

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