Leonardo Tolomeo

collaborators

5 papers

math.AP2025

Quasi invariant Gaussian measures for the nonlinear Schrödinger equation on $T^{2}$

Leonardo Tolomeo, Nicola Visciglia

We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schrödinger equation $i \partial_{t} u + Δ u = ∣ u ∣^{2 k} u$ posed on $T^{2}$ . In partic…

math.AP2025

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 $$ dρ…

math.PR2025

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…

math.PR2024

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 $d$ -dimensional torus with weakly interacting focusing quartic potentials whose coupling constants tend to $0$ as we remove regulariza…

math.PR2024

Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation

Justin Forlano, Leonardo Tolomeo

We consider the stochastic damped nonlinear wave equation $\partial_{t}^{2} u + \partial_{t} u + u - Δ u + u^{3} = 2 ⟨ \nabla ⟩^{- s} ξ$ on the two-dimensional torus $\mathb…