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May 2010 Large deviations of the front in a one-dimensional model of X+Y→2X
Jean Bérard, Alejandro F. Ramírez
Ann. Probab. 38(3): 955-1018 (May 2010). DOI: 10.1214/09-AOP502


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, v], where v 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.


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Jean Bérard. Alejandro F. Ramírez. "Large deviations of the front in a one-dimensional model of X+Y→2X." Ann. Probab. 38 (3) 955 - 1018, May 2010.


Published: May 2010
First available in Project Euclid: 2 June 2010

zbMATH: 1203.60144
MathSciNet: MR2674992
Digital Object Identifier: 10.1214/09-AOP502

Primary: 60F10 , 60K35

Keywords: large deviations , regeneration techniques , sub-additivity

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 3 • May 2010
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