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

Subtitle:
Phase transition of the speed
Abstract:

We prove the sharpness of the phase transition for the speed in biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least two, 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 ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1002/cpa.21491

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Institution:
Courant Institute
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Institution:
University of Oxford
Oxford college:
St Hugh's College
Department:
Mathematical, Physical & Life Sciences Division - Statistics
Publisher:
Wiley Publisher's website
Journal:
Communications on Pure and Applied Mathematics Journal website
Volume:
67
Issue:
2
Pages:
173-245
Publication date:
2013
DOI:
EISSN:
1097-0312
ISSN:
0010-3640
URN:
uuid:5dc5bf1a-7e34-4c6b-afa8-8d861ee8962d
Local pid:
ora:7597

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