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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fluctuations of the front in a one dimensional model of $ X+Y\to 2X$


Authors: Francis Comets, Jeremy Quastel and Alejandro F. Ramírez
Journal: Trans. Amer. Math. Soc. 361 (2009), 6165-6189
MSC (2000): Primary 82C22, 82C41; Secondary 82C24, 60K05, 60G50
Published electronically: May 1, 2009
MathSciNet review: 2529928
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Abstract: We consider a model of the reaction $ X+Y\to 2X$ on the integer lattice in which $ Y$ particles do not move while $ X$ particles move as independent continuous time, simple symmetric random walks. $ Y$ particles are transformed instantaneously to $ X$ particles upon contact. We start with a fixed number $ a\ge 1$ of $ Y$ particles at each site to the right of the origin. We prove a central limit theorem for the rightmost visited site of the $ X$ particles up to time $ t$ and show that the law of the environment as seen from the front converges to a unique invariant measure.


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Additional Information

Francis Comets
Affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 7- Denis Diderot, 2, Place Jussieu, F-75251 Paris Cedex 05, France
Email: comets@math.jussieu.fr

Jeremy Quastel
Affiliation: Departments of Mathematics and Statistics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 1L2
Email: quastel@math.toronto.edu

Alejandro F. Ramírez
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile
Email: aramirez@mat.puc.cl

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04889-2
PII: S 0002-9947(09)04889-2
Keywords: Regeneration times, interacting particle systems, front propagation
Received by editor(s): April 26, 2007
Received by editor(s) in revised form: July 30, 2008
Published electronically: May 1, 2009
Additional Notes: The first author was partially supported by CNRS, UMR 7599 and by ECOS-Conicyt grant CO5EO2
The second author was partially supported by NSERC, Canada
The third author was partially supported by Fondo Nacional de Desarrollo Científico y Tecnológico grant 1060738, by Iniciativa Científica Milenio P04-069-F, and by ECOS-Conicyt grant CO5EO2
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.