9 papers
Limit shapes for centrally excited walks
Ahmed Bou-Rabee, Yuval Peres, Tuan-Minh Nguyen +1
A centrally excited random walk on moves like simple random walk, except that its first step from each site other than the origin has a drift of fixed size toward it.…
Once-reinforced random walk on has range exponent at least
Ahmed Bou-Rabee, Yuval Peres
In once-reinforced random walk, introduced by Davis (1990), every edge starts with weight one and is assigned weight after its first crossing. At each step the walker choo…
The randomly oriented Manhattan lattice in 2D is transient
Ahmed Bou-Rabee, Yuval Peres
Independently orient each horizontal and vertical line of by a fair coin. A walker chooses one of the two lines through its current position with equal probability a…
Eulerian walkers on have range exponent
Ahmed Bou-Rabee, Yuval Peres
In the Eulerian walker model (also known as rotor walk), each site of the square lattice begins with an arrow pointing to one of its four neighbors. A walker that starts at the ori…
Harnack inequality for -harmonic functions: probabilistic and analytic approaches
Yuval Peres, Han Wang
We survey analytic and probabilistic approaches to the Harnack inequality for -harmonic functions, , with particular attention to the dependence of the constants on and…
Mixing times of step-reinforced random walks
Yuval Peres, Shuo Qin
We study the mixing time of a non-Markovian process, the step-reinforced random walk (SRRW) on a finite group. This process differs from a classical random walk in that at each int…
Divisible sandpiles via random walks in random scenery
Ahmed Bou-Rabee, Yuval Peres, Ecaterina Sava-Huss
We analyze an optimal stopping problem for random walk in random scenery on general graphs, and determine when it has a finite optimum. We use this to extend a theorem of Levine, M…
Transition probabilities of step-reinforced random walks
Yuval Peres, Shuo Qin
The step-reinforced random walk (SRRW) either repeats a uniformly chosen past step or takes a fresh independent step. We consider a generalized SRRW on groups, where the selected p…
Optimal lower bound for the variance of hitting times for simple random walks on graphs
Rafael Chiclana, Yuval Peres
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the…