Abstract
Let \({r: S\times S\to \mathbb R_{+}}\) be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For α > 1, let \({g: \mathbb N\to \mathbb R_{+}}\) be given by g(0) = 0, g(1) = 1, g(k) = (k/k − 1)α, k ≥ 2. Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r (x, y). Let N stand for the total number of particles. In the stationary state, as \({N\uparrow\infty}\) , all particles but a finite number accumulate on one single site. We show in this article that in the time scale N 1+α the site which concentrates almost all particles evolves as a random walk on S whose transition rates are proportional to the capacities of the underlying random walk.
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Beltrán, J., Landim, C. Metastability of reversible condensed zero range processes on a finite set. Probab. Theory Relat. Fields 152, 781–807 (2012). https://doi.org/10.1007/s00440-010-0337-0
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DOI: https://doi.org/10.1007/s00440-010-0337-0