Related papers: Existence of quasi-stationary measures for asymmet…

We study nonlinear energy transfer and the existence of stationary measures in a class of degenerately forced SDEs on $\mathbb R^d$ with a quadratic, conservative nonlinearity $B(x,x)$ constrained to possess various properties common to…

We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each \rho\in ]0,1[, we establish uniqueness of the…

We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…

There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and…

A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…

We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…

In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological…

We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…

We provide a class of examples of interacting particle systems on $\mathbb{Z}^d$, for $d\in\{1,2\}$, that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting…

This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an unperturbed system will survive. Under the assumption for…

We study conservative particle systems on W^S, where S is countable and W = {0, ..., N} or the natural numbers. The rate of a particle moving from site x to site y is given by p(x,y) b(eta_x, eta_y), where eta_z is the number of particles…

We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of…

We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…

Let $f$ be a holomorphic endomorphism of $\mathbb P^k$ of degree $d.$ For each quasi-attractor of $f$ we construct a finite set of currents with attractive behaviors. To every such an attracting current is associated an equilibrium measure…

The present paper is devoted to the large deviation principle (LDP), with particular emphasis on the regularity of the quasi-potential for densities of stationary and quasi-stationary distributions of randomly perturbed dynamical systems.…

We study a new non-equilibrium dynamical model: a marked continuous contact model in $d$-dimensional space ($d \ge 3$). We prove that for certain values of rates (the critical regime) this system has the one-parameter family of invariant…