3 citations · 4 across the 4 of their papers we have counts for
4 papers · 1 filter
A permuted random walk exits faster
Richard Pymar, Perla Sousi
Let be a permutation of . We consider the Markov chain which jumps from to or , equally likely. When is at 0 it jumps to ei…
Hunter, Cauchy Rabbit, and Optimal Kakeya Sets
Yakov Babichenko, Yuval Peres, Ron Peretz +2
A planar set that contains a unit segment in every direction is called a Kakeya set. We relate these sets to a game of pursuit on a cycle . A hunter and a rabbit move on the…
Mobile Geometric Graphs: Detection, Coverage and Percolation
Yuval Peres, Alistair Sinclair, Perla Sousi +1
We consider the following dynamic Boolean model introduced by van den Berg, Meester and White (1997). At time 0, let the nodes of the graph be a Poisson point process in R^d with c…
Collisions of Random Walks
Martin T. Barlow, Yuval Peres, Perla Sousi
A recurrent graph has the infinite collision property if two independent random walks on , started at the same point, collide infinitely often a.s. We give a simple criterio…