Phase transition for invariant measures of the focusing Schr\" odinger equation

L Tolomeo, H Weber - arxiv preprint arxiv:2306.07697, 2023 - arxiv.org
We consider the Gibbs measure for the focusing nonlinear Schr\" odinger equation on the
one-dimensional torus $\mathbb T $, that was introduced in a seminal paper by Lebowitz …

Hyperbolic -model on the plane

T Oh, L Tolomeo, Y Wang, G Zheng - arxiv preprint arxiv:2211.03735, 2022 - arxiv.org
We study the hyperbolic $\Phi^{k+ 1} _2 $-model on the plane. By establishing coming down
from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we …

Invariant Gibbs measures for -dimensional wave maps into Lie groups

B Bringmann - arxiv preprint arxiv:2309.06261, 2023 - arxiv.org
We discuss the $(1+ 1) $-dimensional wave maps equation with values in a compact Lie
group. The corresponding Gibbs measure is given by a Brownian motion on the Lie group …

Central limit theorem for the focusing -measure in the infinite volume limit

K Seong, P Sosoe - arxiv preprint arxiv:2411.07840, 2024 - arxiv.org
We study the fluctuations of the focusing $\Phi^ 4$-measure on the one-dimensional torus,
in the infinite volume limit. This measure is the invariant Gibbs measure for the nonlinear …