Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model
Annals of Applied Probability, ISSN: 1050-5164, Vol: 12, Issue: 2, Page: 565-580
2002
- 13Citations
- 3Captures
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Article Description
We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in Z, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate 1, polls its four neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times t < ∞, but the cluster of a fixed site diverges (in diameter) as t → ∞; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0036339031&origin=inward; http://dx.doi.org/10.1214/aoap/1026915616; https://projecteuclid.org/journals/annals-of-applied-probability/volume-12/issue-2/Clusters-and-recurrence-in-the-two-dimensional-zero-temperature-stochastic/10.1214/aoap/1026915616.full; http://projecteuclid.org/download/pdf_1/euclid.aoap/1026915616; https://dx.doi.org/10.1214/aoap/1026915616; https://projecteuclid.org/access-suspended
Institute of Mathematical Statistics
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