Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

Tadahiro Oh; Laurent Thomann

Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

Tadahiro Oh, Laurent Thomann

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.

Original language	English
Number of pages	21
Journal	Annales de la Faculte des Sciences de Toulouse
Volume	29
Issue number	1
Publication status	Published - 24 Jul 2020

Keywords

nonlinear wave equation
nonlinear Klein-Gordon equation
Gibbs measure
Wick ordering
Hermite polynomial
white noise functional
weak universality

Access to Document

1703.10452Accepted author manuscript, 316 KB

https://arxiv.org/abs/1703.10452

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

Cite this

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title = "Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations",

abstract = "We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.",

keywords = "nonlinear wave equation, nonlinear Klein-Gordon equation, Gibbs measure, Wick ordering, Hermite polynomial, white noise functional, weak universality",

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T1 - Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

AU - Oh, Tadahiro

AU - Thomann, Laurent

PY - 2020/7/24

Y1 - 2020/7/24

N2 - We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.

AB - We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.

KW - nonlinear wave equation

KW - nonlinear Klein-Gordon equation

KW - Gibbs measure

KW - Wick ordering

KW - Hermite polynomial

KW - white noise functional

KW - weak universality

M3 - Article

VL - 29

JO - Annales de la Faculte des Sciences de Toulouse

JF - Annales de la Faculte des Sciences de Toulouse

SN - 2258-7519

IS - 1

ER -

Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

Abstract

Keywords

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this