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Fluctuations of the Front in a One Dimensional Model of X + Y → 2X

Francis Comets, Jeremy Quastel and Alejandro F. Ramírez
Transactions of the American Mathematical Society
Vol. 361, No. 11 (Nov., 2009), pp. 6165-6189
Stable URL: http://www.jstor.org/stable/40302951
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Fluctuations of the Front in a One Dimensional Model of X + Y → 2X
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Abstract

We consider a model of the reaction X + Y → 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 α ≥ 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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