EVENT DETAILS AND ABSTRACT

Title: Percolative properties of Brownian interlacements and its vacant set
Speaker: Xinyi Li
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

In this talk, I will give a brief introduction to Brownian interlacements, and investigate various percolative properties regarding this model. Roughly speaking, Brownian interlacements can be described as a certain Poissonian cloud of doubly-infinite continuous trajectories in the d-dimensional Euclidean space, d greater or equal to 3, with the intensity measure governed by a level parameter. We are interested in both the interlacement set, which is an enlargement (“the sausages”) of the union of the trace in the aforementioned cloud of trajectories, and the vacant set, which is the complement of the interlacement set. I will talk about the following results: 1) The interlacement set is “well-connected”, i.e., any two “sausages” in d-dimensional Brownian interlacements, can be connected via no more than ceiling((d − 4)/2) intermediate sausages almost surely. 2) The vacant set undergoes a non-trivial percolation phase transition when the level parameter varies.