Seminar

Language English
From 2011/03/17 13:30
To 2011/03/17 15:00
PlaceRoom 108, Building No.3, Faculty of Science, Kyoto University
Seminar NameKansai Probability Theory Seminar
Title Phase transition for the speed of the biased random walk on the supercritical percolation cluster　
Field Analysis
Other
SpeakersAlexander Fribergh
AffiliationCourant Institute
AbstractIn this joint work with Alan Hammond, we prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on . That is, for each , and for any supercritical parameter , we prove the existence of a critical strength for the bias, such that, below this value, the speed is positive, and, above this value, it is zero. We identify the value of the critical bias explicitly, and, in the sub-ballistic regime, we find the polynomial order in the distance moved by the particle. Each of these conclusions is obtained by investigating the geometry of the traps that are most effective at delaying the walk.
A key element in proving our results is to understand that, on large scales, the particle trajectory is essentially one-dimensional; we prove such a "dynamic renormalization" statement in a much stronger form than was previously known.
Note時間、場所ともに通常と異なりますので、ご注意下さい。
Linkhttp://www-an.acs.i.kyoto-u.ac.jp/~hino/probability/seminar/index_j.html