57 citations · 220 across the 14 of their papers we have counts for
21 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 penalize…
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…
Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup
Caio Alves, Artem Sapozhnikov
It has been recently understood (arXiv:1212.2885, arXiv:1310.4764, arXiv:1410.0605) that for a general class of percolation models on satisfying suitable decoupling…
Kesten's incipient infinite cluster and quasi-multiplicativity of crossing probabilities
Deepan Basu, Artem Sapozhnikov
In this paper we consider Bernoulli percolation on an infinite connected bounded degrees graph . Assuming the uniqueness of the infinite open cluster and a quasi-multiplicativit…
On Brownian motion, simple paths, and loops
Artem Sapozhnikov, Daisuke Shiraishi
We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove…
Mixing time for the random walk on the range of the random walk on tori
Jiří Černý, Artem Sapozhnikov
Consider the subgraph of the discrete -dimensional torus of size length , , induced by the range of the simple random walk on the torus run until the time . We p…
Crossing probabilities for critical Bernoulli percolation on slabs
Deepan Basu, Artem Sapozhnikov
We prove that in the critical Bernoulli percolation on two dimensional lattice slabs the probabilities of open left-right crossings of rectangles with any given aspect ratio are un…
Random walks on infinite percolation clusters in models with long-range correlations
Artem Sapozhnikov
For a general class of percolation models with long-range correlations on , , introduced in arXiv:1212.2885, we establish regularity conditions of Barlow arXi…
Phase transition in loop percolation
Yinshan Chang, Artëm Sapozhnikov
We are interested in the clusters formed by a Poisson ensemble of Markovian loops on infinite graphs. This model was introduced and studied in [LeJ12] and [LL12]. It is a model wit…
Quenched invariance principle for simple random walk on clusters in correlated percolation models
Eviatar Procaccia, Ron Rosenthal, Artem Sapozhnikov
We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range cor…
On chemical distances and shape theorems in percolation models with long-range correlations
Alexander Drewitz, Balazs Rath, Artem Sapozhnikov
In this paper we provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical dist…
Local percolative properties of the vacant set of random interlacements with small intensity
Alexander Drewitz, Balazs Rath, Artem Sapozhnikov
Random interlacements at level u is a one parameter family of connected random subsets of Z^d, d>=3 introduced in arXiv:0704.2560. Its complement, the vacant set at level u, exhibi…
The effect of small quenched noise on connectivity properties of random interlacements
Balazs Rath, Artem Sapozhnikov
The random interlacements (at level u) is a one parameter family of random subsets of Z^d introduced by Sznitman in arXiv:0704.2560. The vacant set at level u is the complement of…
Cycle structure of percolation on high-dimensional tori
Remco van der Hofstad, Artem Sapozhnikov
In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been establishe…
Connectivity properties of random interlacement and intersection of random walks
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…
Limit theorems for 2D invasion percolation
Michael Damron, Artëm Sapozhnikov
We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence $({\mathbf…
Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters
Michael Damron, Artem Sapozhnikov
We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters…
Relations between invasion percolation and critical percolation in two dimensions
Michael Damron, Artëm Sapozhnikov, Bálint Vágvölgyi
We study invasion percolation in two dimensions. We compare connectivity properties of the origin's invaded region to those of (a) the critical percolation cluster of the origin an…