5 papers
Multi-hop visibility through the vacant set of Poissonian obstacles
Yingxin Mu, Artem Sapozhnikov
We study multi-hop visibility inside the vacant set of three obstacle models in with slow decay of spatial correlations and disparate obstacle geometries: Poisson-Boo…
Critical curve of loop percolation on the -regular tree
Luca Makowiec, Artem Sapozhnikov
We consider clusters formed by a Poisson ensemble of random walk loops on the -regular tree with an intensity parameter and a killing parameter ; the latter penali…
Visibility in Brownain 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 Boolean model. Fo…
Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs
Yingxin Mu, Artem Sapozhnikov
We prove the uniqueness of the infinite connected component for the vacant set of random interlacements on general vertex-transitive amenable transient graphs. Our approach is base…
On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements
Yingxin Mu, Artem Sapozhnikov
We consider connectivity properties of the vacant set of (random) ensembles of Wiener sausages in in the transient dimensions . We prove that the vacant set…