- Phase transition of the speed
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 ...Expand abstract
- Publication status:
- Peer review status:
- Peer reviewed
- Accepted Manuscript
- Copyright holder:
- Wiley Periodicals, Inc.
- Copyright date:
- Copyright © 2013 Wiley Periodicals, Inc.
Phase transition for the speed of the biased random walk on the supercritical percolation cluster
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