Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model |
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Authors: | J. -R. Chazottes F. Redig |
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Affiliation: | (1) CPhT CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France;(2) Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, Postbus 513, 5600 MB Eindhoven, The Netherlands |
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Abstract: | We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation |
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Keywords: | Disagreement percolation exponential law Poisson law Gumbel law large deviations |
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