Fluctuations of the front in a stochastic combustion model |
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Authors: | Francis Comets Jeremy Quastel Alejandro F Ramírez |
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Institution: | a Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 7-Denis Diderot, 2, Place Jussieu, 75251 Paris cedex 05, France b Departments of Mathematics and Statistics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 1L2, Canada c Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile |
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Abstract: | We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2?a?M<∞. Particles move independently as continuous time simple symmetric random walks except that (i) when a particle jumps to a site which has not been previously visited by any particle, it branches into a particles, (ii) when a particle jumps to a site with M particles, it is annihilated. We start from a configuration where all sites to the left of the origin have been previously visited and study the law of large numbers and central limit theorem for rt, the rightmost visited site at time t. The proofs are based on the construction of a renewal structure leading to a definition of regeneration times for which good tail estimates can be performed. |
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Keywords: | primary 82C22 82B41 secondary 82B24 60K35 60G99 |
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