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Phase transition for the speed of the biased random walk on the supercritical percolation cluster

Abstract:

We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least 2, and for any supercritical parameter p > p_c, we prove the existence of a critical strength for the bias, such that, below this value, the speed is positive, and, above the value, it is zero. We identify the value of the critical bias explicitly, and, in the sub-ballistic regime, we find the polynomial order of the distance moved...

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Publication status:
Published

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Publisher copy:
10.1002/cpa.21491

Authors


Fribergh, A More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Journal:
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume:
67
Issue:
2
Pages:
173-245
Publication date:
2011-03-07
DOI:
EISSN:
1097-0312
ISSN:
0010-3640
URN:
uuid:1953507d-2764-4117-971f-364690169680
Source identifiers:
204298
Local pid:
pubs:204298
Keywords:

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