Abstract
This paper is a sequel to [5] and [6]. 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., [11] or [8]). 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 [5] and [6], 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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Dedicated to Frank Spitzer on his 60th birthday
Partially supported by the National Science Foundation under Grant DMS-831080
Partially supported by the National Science Foundation under Grant DMS-841317
Partially supported by the National Science Foundation under Grant DMS-830549
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Bramson, M., Theodore Cox, J. & Griffeath, D. Occupation time large deviations of the voter model. Probab. Th. Rel. Fields 77, 401–413 (1988). https://doi.org/10.1007/BF00319297
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DOI: https://doi.org/10.1007/BF00319297
Keywords
- Lower Bound
- Stochastic Process
- Decay Rate
- Probability Theory
- High Dimension