Metastability of reversible condensed zero range processes on a finite set
By J. Beltr'an, C. Landim. 2009
87 citations recorded by the source corpus.
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 N1+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.
Subfields: Mathematical Physics, Molecular Biology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fbf681d630a109713720d5409c96e598019b241f
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Citations in the corpus
- A Dirichlet principle for non reversible Markov chains and some recurrence theorems (2011, methodology): “In a completely different direction, relying on the Dirichlet principle presented in this article we prove in [9] the metastable behavior of the condensate in supercritical asymmetric zero range processes, extending to the non-reversible case the results proved in [3].”