arXiv subjects

Elena Kosygina

Publications and source records attributed to Elena Kosygina.

22 records · Page 2Linked to original sources

arXiv2011

Crossing velocities for an annealed random walk in a random potential

We consider a random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice. The walk starts at the origin and is conditioned to hit a remote location y on the lattice. We prove that the expected time under the annealed path measure needed by the random walk to reach y grows only linearly in the distance from y to the origin. In dimension one we show the existence of the asymptotic positive speed.

math.PR↗

arXiv2011

Limit laws of transient excited random walks on integers

We consider excited random walks (ERWs) on integers with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [KZ08] have shown that when the total expected drift per site, delta, is larger than 1 then ERW is transient to the right and, moreover, for delta>4 under the averaged measure it obeys the Central Limit Theorem. We show that when delta in (2,4] the limiting behavior of an appropriately centered and scaled excited random walk under the averaged measure is described by a strictly stable law with parameter delta/2. Our method also extends the results obtained by Basdevant and Singh [BS08b] for delta in (1,2] under the non-negativity assumption to the setting which allows both positive and negative cookies.

math.PR↗

arXiv2010

Lyapunov exponents of Green's functions for random potentials tending to zero

We consider quenched and annealed Lyapunov exponents for the Green's function of $-Δ+γV$, where the potentials $V(x), x\in\Z^d$, are i.i.d. nonnegative random variables and $γ>0$ is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like $c\sqrtγ$ as $γ$ tends to 0. Here the constant $c$ is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wei-Min Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.

math.PR↗

arXiv2008

Positively and negatively excited random walks on integers, with branching processes

We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.

math.PR↗