Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Fluctuations of the front in a one dimensional model of $X+Y\to 2X$
HTML articles powered by AMS MathViewer

by Francis Comets, Jeremy Quastel and Alejandro F. Ramírez PDF
Trans. Amer. Math. Soc. 361 (2009), 6165-6189 Request permission

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.
References
Similar Articles
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
  • MR Author ID: 322635
  • 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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 6165-6189
  • MSC (2000): Primary 82C22, 82C41; Secondary 82C24, 60K05, 60G50
  • DOI: https://doi.org/10.1090/S0002-9947-09-04889-2
  • MathSciNet review: 2529928