LARGE DEVIATIONS OF THE FRONT IN A ONE-DIMENSIONAL MODEL OF X plus Y → 2X

• 成果类型: Article
• 署名作者: Berard, Jean; Ramirez, Alejandro F.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Pontificia Universidad Catolica de Chile
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP502
• 发表日期: 2010
• 页码: 955-1018
• 关键词: random-walk; propagation; fluctuations; BEHAVIOR

摘要

We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction X + Y -> 2X on the integer lattice in which Y particles do not move while X particles move as independent simple continuous time random walks of total jump rate 2. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zero set of the rate function is the interval [0, nu vertical bar. where nu is the velocity of the front given by the law of large numbers. We also give more precise estimates for the rate of decay of the slowdown probabilities. Our results indicate a gapless property of the generator of the process as seen from the front, as it happens in the context of nonlinear diffusion equations describing the propagation of a pulled front into an unstable state.