The one dimensional n.n. simple exclusion process with generator \epsilon^{-2}L_0+\epsilon^{-1}1L_a, \epsilon > 0, is considered, L_0 and L_a respectively the generators of the symmetric and totally asymmetric simple exclusion processes. Propagation of chaos and convergence to the Burgers equation with viscosity are proven in the limit when \epsilon goes to zero. The density fluctuation field is shown to converge to a generalized Ornstein Uhlenbeck process with mean zero. The time asymptotic covariance kernel is explicitly computed for traveling wave profiles and the result indicates that the shock profile is stable while its space location fluctuates around its average position like a brownian motion. Its diffusion coefficient is explicitly computed.

The weakly asymmetric simple exclusion process

DE MASI, Anna
;
1989

Abstract

The one dimensional n.n. simple exclusion process with generator \epsilon^{-2}L_0+\epsilon^{-1}1L_a, \epsilon > 0, is considered, L_0 and L_a respectively the generators of the symmetric and totally asymmetric simple exclusion processes. Propagation of chaos and convergence to the Burgers equation with viscosity are proven in the limit when \epsilon goes to zero. The density fluctuation field is shown to converge to a generalized Ornstein Uhlenbeck process with mean zero. The time asymptotic covariance kernel is explicitly computed for traveling wave profiles and the result indicates that the shock profile is stable while its space location fluctuates around its average position like a brownian motion. Its diffusion coefficient is explicitly computed.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/18291
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 69
social impact