Stretched Exponential Relaxation in the Biased Random Voter Model

Details Stretched Exponential Relaxation in the Biased Random Voter Model Stretched Exponential Relaxation in the Biased Random Voter Model

1999-02-27

arxiv.org/abs/math-ph/9903002v1

J. Phys. A32, 7653-7664 (1999)

Physics

Mathematical Physics

14 pages, AMS-LaTeX

Scientific paper

10.1088/0305-4470/32/44/304

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).

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