Leonardo Tolomeo

activity

20232026

collaborators

10 papers

math.AP2026

Radial $Φ^{4}$ models in supercritical regimes

Tadahiro Oh, Leonardo Tolomeo, Nikolay Tzvetkov +1

We consider the $Φ_{d}^{4}$ measure under radial symmetry on the unit ball, formally given by $$dρ(u) = \frac 1 Z \exp\Big( - \frac 14 \int_{B_1} |u|^4 dx - \frac 12 \int_{B_1} |\nabla…

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.AP2024

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…

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…

math.AP2024

Sharp quasi-invariance threshold for the cubic Szegő equation

James Coe, Leonardo Tolomeo

We consider the 1-dimensional cubic Szegő equation with data distributed according to the Gaussian measure with inverse covariance operator $(1 - \partial_{x}^{2})^{\frac{s}{2}}$ , where $s>\f…

math.AP2023

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 normalizabil…

math.PR2023

Ergodicity for the hyperbolic $P (Φ)_{2}$ -model