5 papers
On the maximum visibility in a ball through the vacant set of Poissonian obstacles
Yingxin Mu, Artem Sapozhnikov
We study the maximum visibility in a ball inside the vacant set of three obstacle models in with slow decay of spatial correlations and disparate obstacle geometries:…
On the visibility window for Brownian interlacements, Poisson cylinders and Boolean models
Yingxin Mu, Artem Sapozhnikov
We study visibility inside the vacant set of three models in with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean m…
Indistinguishability of unbounded components in the occupied and vacant sets of Boolean models on symmetric spaces
Yingxin Mu, Artem Sapozhnikov
We study Boolean models on Riemannian symmetric spaces driven by homogeneous insertion- or deletion-tolerant point processes. We prove that in both the set covered by the balls (th…
The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions
Artem Sapozhnikov
This note is motivated by results in arXiv:math/0608132 and arXiv:0806.2425 about global relations between the invasion percolation cluster (IPC) and the incipient infinite cluster…
On the transience of random interlacements
Balázs Ráth, Artëm Sapozhnikov
We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite…