Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …
Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation
T Oh, M Okamoto, N Tzvetkov - Annales de l'Institut Henri Poincare …, 2024 - projecteuclid.org
We study the nonlinear wave equation (NLW) on the two-dimensional torus T 2 with
Gaussian random initial data on H s (T 2)× H s− 1 (T 2), s< 0, distributed according to the …
Gaussian random initial data on H s (T 2)× H s− 1 (T 2), s< 0, distributed according to the …
[HTML][HTML] A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations
We consider the defocusing nonlinear Schrödinger equations on the two-dimensional
compact Riemannian manifold without boundary or a bounded domain in R^ 2 R 2. Our aim …
compact Riemannian manifold without boundary or a bounded domain in R^ 2 R 2. Our aim …
Invariant Gibbs measures for the 2- defocusing nonlinear wave equations
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 …
In particular, we construct invariant Gibbs measures for the renormalized so-called Wick …
On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can
not be displayed here. See the abstract in the paper.) We study convergence problems for …
not be displayed here. See the abstract in the paper.) We study convergence problems for …
A remark on Gibbs measures with log-correlated Gaussian fields
We study Gibbs measures with log-correlated base Gaussian fields on the $ d $-
dimensional torus. In the defocusing case, the construction of such Gibbs measures follows …
dimensional torus. In the defocusing case, the construction of such Gibbs measures follows …
[HTML][HTML] Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus
We study an optimal mass threshold for normalizability of the Gibbs measures associated
with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional …
with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional …
Invariance of white noise for KdV on the line
We consider the Korteweg–de Vries equation with white noise initial data, posed on the
whole real line, and prove the almost sure existence of solutions. Moreover, we show that …
whole real line, and prove the almost sure existence of solutions. Moreover, we show that …
Gibbs measure for the focusing fractional NLS on the torus
We study the construction of the Gibbs measures for the focusing mass-critical fractional
nonlinear Schrödinger equation on the multidimensional torus. We identify the sharp mass …
nonlinear Schrödinger equation on the multidimensional torus. We identify the sharp mass …
Optimal divergence rate of the focusing Gibbs measure
We study the focusing Gibbs measure with critical/supercritical potentials. In particular, we
prove asymptotic formulae for the frequency approximation of the partition function, which …
prove asymptotic formulae for the frequency approximation of the partition function, which …