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math.PR2009★ 4 cited
Is the critical percolation probability local?
Itai Benjamini, Asaf Nachmias, Yuval Peres
We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular…
math.PR2004
Fluctuation of planar Brownian loop capturing large area
Alan Hammond, Yuval Peres
We consider a planar Brownian loop that is run for a time and conditioned on the event that its range encloses the unusually high area of , with being large. We s…
math.PR2004
Shuffling by semi-random transpositions
Elchanan Mossel, Yuval Peres, Alistair Sinclair
In the cyclic-to-random shuffle, we are given n cards arranged in a circle. At step k, we exchange the k'th card along the circle with a uniformly chosen random card. The problem o…