6 papers · 1 filter
Radial models in supercritical regimes
Tadahiro Oh, Leonardo Tolomeo, Nikolay Tzvetkov +1
We consider the measure under radial symmetry on the unit ball, formally given by $$dρ(u) = \frac 1 Z \exp\Big( - \frac 14 \int_{B_1} |u|^4 dx - \frac 12 \int_{B_1} |\nabla…
Quasi invariant Gaussian measures for the nonlinear Schrödinger equation on
Leonardo Tolomeo, Nicola Visciglia
We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schrödinger equation posed on . In partic…
A remark on the log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation
Guopeng Li, Jiawei Li, Leonardo Tolomeo
We consider the question of showing a log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation built by Lebowitz-Rose-Speer (1988), formally given by $$ dρ…
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…
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 , where $s>\f…
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…