33 citations · 116 across the 14 of their papers we have counts for
15 papers
Phase transition for invariant measures of the focusing Schrödinger equation
Leonardo Tolomeo, Hendrik Weber
We consider the Gibbs measure for the focusing nonlinear Schrödinger equation on the one-dimensional torus , that was introduced in a seminal paper by Lebowitz, Rose and…
Focusing Gibbs measures with harmonic potential
Tristan Robert, Kihoon Seong, Leonardo Tolomeo +1
In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for norma…
Hyperbolic -model on the plane
Tadahiro Oh, Leonardo Tolomeo, Yuzhao Wang +1
We study the hyperbolic -model on the plane. By establishing coming down from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we firs…
Yet another notion of irregularity through small ball estimates
Marco Romito, Leonardo Tolomeo
We introduce a new notion of irregularity of paths, in terms of control of growth of the size of small balls by means of the occupation measure of the path. This notion ensures Bes…
Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations
Justin Forlano, Leonardo Tolomeo
We consider the Cauchy problem for the fractional nonlinear Schrödinger equation (FNLS) on the one-dimensional torus with cubic nonlinearity and high dispersion parameter , s…
Stochastic quantization of the -model
Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study the construction o…
On the unique ergodicity for a class of 2 dimensional stochastic wave equations
Justin Forlano, Leonardo Tolomeo
We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the -dimensional torus. The noise…
A remark on Gibbs measures with log-correlated Gaussian fields
Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo
We study Gibbs measures with log-correlated base Gaussian fields on the -dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson's…
Maximum power heat engines and refrigerators in the fast-driving regime
Vasco Cavina, Paolo A. Erdman, Paolo Abiuso +2
We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the op…
Focusing -model with a Hartree-type nonlinearity
Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) Lebowitz, Rose, and Speer (…
Global dynamics for the two-dimensional stochastic nonlinear wave equations
Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh +1
We study global-in-time dynamics of the stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing, posed on the two-dimensional torus. Our goal in…
Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain
Leonardo Tolomeo
We study the two-dimensional wave equation with cubic nonlinearity posed on , with space-time white noise forcing. After a suitable renormalisation of the nonlinearity…
Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise
Leonardo Tolomeo
In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the -dimensional torus. This class includes t…
A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds
Alex Amenta, Leonardo Tolomeo
Given a sequence of complete Riemannian manifolds of the same dimension, we construct a complete Riemannian manifold such that for all the -norm…
Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus
Tadahiro Oh, Philippe Sosoe, Leonardo Tolomeo
We study an optimal mass threshold for normalizability of the Gibbs measures associated with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional torus.…