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 …

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 …

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 …

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 …

(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 …

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 …

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 …

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 …

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 …

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 …