Encontrados 9 documentos, a visualizar página 1 de 1
A stochastic Burgers equation from a class of microscopic interactions
Gonçalves, Patrícia; Jara, Milton; Sethuraman, SunderDocumento submetido para revisão pelos pares. A publicar em Annals of Probability. ISSN 0091-1798 ; We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order $O(n^\gamma)$ for $1/2<\gamma\leq 1$, we show...
Scaling limits of additive functionals of interacting particle systems
Gonçalves, Patrícia; Jara, MiltonEm publicação ; Using the renormalization method introduced in [arXiv:1003.4478v1], we prove what we call the local Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension d=1. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics...
Nonlinear fluctuations of interacting particle systems
Gonçalves, Patrícia; Jara, MiltonEm publicação ; We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states. As an applica...
Crossover to the KPZ equation
Gonçalves, Patrícia; Jara, MiltonWe characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The co...
Density fluctuations for a zero-range process on the percolation cluster
Gonçalves, Patrícia; Jara, MiltonWe prove that the density fluctuations for a zero-range process evolving on the $d$-dimensional supercritical percolation cluster, with $d\geq{3}$, are given by a generalized Ornstein-Uhlenbeck process in the space of distributions $\mathcal{ S}'(\mathbb {R}^d)$.
The crossover to the KPZ equation
Gonçalves, Patrícia; Jara, MiltonIn this paper we consider the one-dimensional weakly asymmetric simple exclusion process under the invariant state $\nu_{\rho}$: the Bernoulli product measure of parameter $\rho\in{(0,1)}$. We show that the limit density field is governed by an Ornstein-Uhlenbeck process for strength asymmetry $n^{2-\gamma}$ if $\gamma\in(1/2,1)$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. From this re...
Universality of KPZ equation and renormalization techniques in interacting part...
Gonçalves, Patrícia; Jara, MiltonIn these notes we use renormalization techniques to derive a second order Boltzmann-Gibbs Principle which allow us to characterize the equilibrium fluctuations of weakly asymmetric exclusion processes as within the KPZ universality class.
Crossover to the KPZ equation
Gonçalves, Patrícia; Jara, MiltonWe consider the weakly asymmetric simple exclusion process and we show that the density field is governed by an Ornstein-Uhlenbeck process for strength asymmetry n2-γ if γϵ (1=2; 1), while for γ= 1=2 it is an energy solution of the KPZ equation.
Scaling limits for gradient systems in random environment
Gonçalves, Patrícia; Jara, MiltonIt is well known that the hydrodynamic limit of an interacting particle system satisfying a gradient condition (such as the zero-range process or the symmetric simple exclusion process) is given by a possibly non-linear parabolic equation and the equilibrium fluctuations from this limit are given by a generalized Ornstein-Uhlenbeck process. We prove that in the presence of a symmetric random environment, these ...
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