8 papers
Cancellations for dispersive PDEs with random initial data
Yvain Bruned, Leonardo Tolomeo
In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The ma…
Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps
Van Duong Dinh, Nicolas Rougerie, Leonardo Tolomeo +1
In this paper, we investigate the Gibbs measures associated with the focusing nonlinear Schrödinger equation with an anharmonic potential. We establish a dichotomy for normalizabi…
Quasi invariant Gaussian measures for the nonlinear Schrödinger equation on
Leonardo Tolomeo, Nicola Visciglia
We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schrödinger equation posed on . In part…
A remark on the log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation
Guopeng Li, Jiawei Li, Leonardo Tolomeo
We consider the question of showing a log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation built by Lebowitz-Rose-Speer (1988), formally given by $$ d…
Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations
James Coe, Martin Hairer, Leonardo Tolomeo
We study the qualitative properties of solutions to the 2D stochastic Navier-Stokes equations with forcing that is white in time and coloured in space. Our main result shows that t…
Critical threshold for weakly interacting log-correlated focusing Gibbs measures
Damiano Greco, Tadahiro Oh, Liying Tao +1
We study log-correlated Gibbs measures on the -dimensional torus with weakly interacting focusing quartic potentials whose coupling constants tend to as we remove regulariza…