Occupation time large deviations of the voter model
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This paper is a sequel to  and . We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model ζt (see e.g.,  or ). In keeping with our previous results, we show that the large deviations are “classical” in high dimensions (d≧5 for ζt) but “fat” in low dimensions (d≦4). Interaction distinguishes the voter model from the independent particle systems of  and , and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.
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- 1.Arratia R.: Symmetric exclusion processes: a comparison inequality and a large deviation result. Ann. Probab. 13, 53–61 (1985)Google Scholar
- 2.Bramson M., Cox J. T., Griffeath D.: Consolidation rates for two interacting systems in the plane. Probab. Th. Rel. Fields 73, 613–625 (1986)Google Scholar
- 3.Bramson M., Griffeath D: Asymptotics for interacting particle systems on Zd. Z. Wahrscheinlichkeitstheor. Verw. Geb. 53, 183–196 (1980)Google Scholar
- 4.Cox J.T., Griffeath D.: Occupation time limit theorems for the voter model. Ann. Probab. 11, 876–893 (1983)Google Scholar
- 5.Cox J.T., Griffeath D.: Large deviations for Poisson systems of independent random walks. Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 543–558 (1984)Google Scholar
- 6.Cox J.T., Griffeath, D.: Occupation times for critical branching Brownian motions. Ann. Probab. 13, 1108–1132 (1985)Google Scholar
- 7.Cox J.T., Griffeath D.: Large deviations for some infinite particle system occupation times. Contemp. Math. 41, 43–54 (1985)Google Scholar
- 8.Cox J.T., Griffeath D.: Diffusive clustering in the two dimensional voter model. Ann. Probab. 14, 347–370 (1986)Google Scholar
- 9.Donsker M., Varadhan S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, IV. Comm. Pure Appl. Math. 36, 183–312 (1983)Google Scholar
- 10.Van den Berg, J., Kesten H.: Inequalities with applications to percolation and reliability. J. Appl. Probab. 22, 556–599 (1985)Google Scholar
- 11.Liggett T.M.: Interacting Particle Systems. Berlin Heidelberg New York: Springer 1985Google Scholar