9 papers
Exponential decay of mass for inertial coalescing particles with Hamiltonian noise
Sandra Cerrai, Franco Flandoli, Mengzi Xie
We study a system of inertial particles on a two-dimensional torus $\T^2$, evolving under a second-order stochastic dynamics with position-dependent friction and noise ampl…
The inertial Itô drift and its applications to particle collision
Sandra Cerrai, Franco Flandoli, Mengzi Xie
The small mass limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time going to zero, leads to a first order system with an additiona…
Parabolic scaling of a stochastic wave map with co-normal noise: limit and fluctuations
Sandra Cerrai, Mengzi Xie
This paper investigates the parabolic scaling limit of a damped stochastic wave map from the real line into the two-dimensional sphere, perturbed by multiplicative Gaussian noise o…
The small-mass limit for some constrained wave equations with nonlinear conservative noise
Sandra Cerrai, Mengzi Xie
We study the small-mass limit, also known as the Smoluchowski-Kramers diffusion approximation (see \cite{kra} and \cite{smolu}), for a system of stochastic damped wave equations, w…
Well-posedness and invariant measure for quasilinear parabolic SPDE on a bounded domain
Mengzi Xie
We study quasilinear parabolic stochastic partial differential equations with general multiplicative noise on a bounded domain in , with homogeneous Dirichlet bound…
On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction
Sandra Cerrai, Mengzi Xie
We investigate the convergence, in the small mass limit, of the stationary solutions of a class of stochastic damped wave equations, where the friction coefficient depends on the s…
Inference of high quantiles of a heavy-tailed distribution from block data
Yongcheng Qi, Mengzi Xie, Jingping Yang
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We pro…
On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction
Sandra Cerrai, Mengzi Xie
We study the validity of a large deviation principle for a class of stochastic nonlinear damped wave equations, of Klein-Gordon type, in the joint small mass and small noise limit.…
Spectral Radii of Products of Random Rectangular Matrices
Yongcheng Qi, Mengzi Xie
We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of th…