We introduce range-controlled random walks with hopping rates depending on the range N,
that is, the total number of previously distinct visited sites. We analyze a one-parameter class …

Electron. J. Probab. 19 (2014), no. 106, DOI: 10.1214/EJP.v19-3272 Page 1 E lectro n i c J o u
r nal o f P r o b ability Electron. J. Probab. 19 (2014), no. 106, 1–20. ISSN: 1083-6489 DOI …

We consider one-dimensional excited random walks (ERWs) with iid Markovian cookie
stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an …

Several phase transitions for excited random walks on the integers are known to be
characterized by a certain drift parameter δ∈\mathbbR. For recurrence/transience the …

We study a stochastic geometric flow that describes a growing submanifold $\mathbb
{M}(t)\subseteq\mathbb {R}^{\mathrm {d}+ 1} $. It is an SPDE that comes from a continuum …

In this paper we consider an excited random walk (ERW) on Z in identically piled periodic
environment. This is a discrete time process on Z defined by parameters …

We consider a nearest-neighbor random walk on Z whose probability x(j) to jump to the right
from site x depends not only on x but also on the number of prior visits j to x. The collection …

The probability that a one dimensional excited random walk in stationary ergodic and elliptic
cookie environment is transient to the right (left) is either zero or one. This solves a problem …

It is a celebrated fact that a simple random walk on an infinite $ k $-ary tree for $ k\geq 2$
returns to the initial vertex at most finitely many times during infinitely many transitions; it is …

We use generalized Ray–Knight theorems, introduced by B. Tóth in 1996, together with
techniques developed for excited random walks as main tools for establishing positive and …