Fluctuations of the front in a one dimensional model of 𝑋+𝑌→2𝑋

Comets, Francis; Quastel, Jeremy; Ramírez, Alejandro

doi:10.1090/S0002-9947-09-04889-2

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

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