5 papers · 1 filter
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…
Sharp quasi-invariance threshold for the cubic SzegÅ equation
James Coe, Leonardo Tolomeo
We consider the 1-dimensional cubic SzegÅ equation with data distributed according to the Gaussian measure with inverse covariance operator , where $s>\…