Estimates of random walk exit probabilities and application to loop-erased random walk.
Exchange symmetries in Motzkin path and bargraph models of copolymer adsorption.
Excited against the tide: a random walk with competing drifts
We study excited random walks in i.i.d. random cookie environments in high dimensions, where the th cookie at a site determines the transition probabilities (to the left and right) for the th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that the limiting...