セミナー

発表言語 英語
開催日 2011年03月16日 13時30分
終了日 2011年03月16日 15時00分
開催場所京都大学理学部3号館 (数学教室) 108号室
セミナー名臨時関西確率論セミナー
タイトル Phase transition for the speed of the biased random walk on the supercritical percolation cluster 
分野 解析
その他
講演者名Alexander Fribergh
講演者所属Courant Institute
概要In 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.
備考時間、場所ともに通常と異なりますので、ご注意下さい。
リンクhttp://www-an.acs.i.kyoto-u.ac.jp/~hino/probability/seminar/index_j.html