A lower bound for disconnection by random interlacements
主 题: A lower bound for disconnection by random interlacements
报告人: 李欣意 (ETH Zürich)
时 间: 2013-12-23 15：00-16:00
地 点: 北京大学理科一号楼 1303（主持人：刘勇）
The talk will be divided into two parts. In the first part, we give a brief introduction to the model of random interlacements, introduced by A.-S. Sznitman in [Ann. Math. vol. 171, pp. 2039-2087]. Random interlacements can be intuitively regarded as the trace of a Poissonian “cloud” of doubly-infinite nearest-neighbour paths on certain weighted graphs, governed by an intensity parameter. The vacant set, defined as the complement of the interlacements, undergoes a non-trivial phase transition with respect to percolative properties. In the second part, we investigate the asymptotic behaviour of the probability that a large body gets disconnected from infinity by the random interlacements on Zd, d ≥ 3, in the percolative regime for the vacant set. Motivated by an application of large deviation principles recently obtained in [arXiv:1304.7477] for the occupation-time profile of random interlacements, we derive an asymptotic lower bound, which brings into play a new version of random interlacements by which a stochastic “fence” is created to accomplish disconnection.