57 citations · 220 across the 14 of their papers we have counts for
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math.PR2015
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…
math.PR2015
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…
math.PR2015
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…