Anisotropic Oriented Percolation In High Dimensions

Gomes Pablo Almeida,Pereira Alan,Sanchis Remy

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS（2020）

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摘要

In this paper we study anisotropic oriented percolation on Z(d) for d >= 4 and show that the local condition for phase transition is closely related to the mean-field condition. More precisely, we show that if the sum of the local probabilities is strictly greater than one and each probability is not too large, then percolation occurs.

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关键词

Anisotropic percolation, high dimensional systems, asymmetric random walk, mean-field

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