23 citations · 88 across the 19 of their papers we have counts for
17 papers · 1 filter
Functional limit theorems for self-interacting random walks
Elena Kosygina, Laure Marêché, Thomas Mountford +1
We consider a wide class of nearest neighbor self-interacting random walks on and show that, under mild conditions, their scaling limits at the process level can be un…
Extension of results on generalized Pólya's urns for polynomially self-repelling walks
Elena Kosygina, Laure Marêché, Thomas Mountford +1
This is a technical note which extends the results of Kosygina, Mountford and Peterson (Ann. Probab., 51(5):1684-1728, 2023, Section 4) about generalized Pólya's urns from a specif…
Convergence of rescaled "true" self-avoiding walks to the Tóth-Werner "true" self-repelling motion
Elena Kosygina, Jonathon Peterson
We prove that the rescaled ``true'' self-avoiding walk converges weakly as goes to infinity to the ``true'' self-repelling…
Convergence and non-convergence of scaled self-interacting random walks to Brownian motion perturbed at extrema
Elena Kosygina, Thomas Mountford, Jonathon Peterson
We use generalized Ray-Knight theorems introduced by Bálint Tóth in 1996 together with techniques developed for excited random walks as main tools for establishing positive and neg…
Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema
Elena Kosygina, Thomas Mountford, Jonathon Peterson
We consider one-dimensional excited random walks (ERWs) with i.i.d. markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW…
Functional limit laws for recurrent excited random walks with periodic cookie stacks
Elena Kosygina, Jonathon Peterson
We consider one-dimensional excited random walks (ERWs) with periodic cookie stacks in the recurrent regime. We prove functional limit theorems for these walks which extend the pre…
A zero-one law for recurrence and transience of frog processes
Elena Kosygina, Martin P. W. Zerner
We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog…
Excited random walks with Markovian cookie stacks
Elena Kosygina, Jonathon Peterson
We consider a nearest-neighbor random walk on whose probability to jump to the right from site depends not only on but also on the number of prior vis…
Excursions and occupation times of critical excited random walks
Dmitry Dolgopyat, Elena Kosygina
The paper considers excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on the critical case for…
Excursions of excited random walks on integers
Elena Kosygina, Martin P. W. Zerner
Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter delta. For recurrence/transience the critical threshol…
Crossing speeds of random walks among "sparse" or "spiky" Bernoulli potentials on integers
Elena Kosygina
We consider a random walk among i.i.d. obstacles on the one dimensional integer lattice under the condition that the walk starts from the origin and reaches a remote location y. Th…
Excited random walks: results, methods, open problems
Elena Kosygina, Martin P. W. Zerner
We consider a class of self-interacting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the d-dimensional integer lattice. T…
Scaling limits of recurrent excited random walks on integers
Dmitry Dolgopyat, Elena Kosygina
We describe scaling limits of recurrent excited random walks (ERWs) on integers in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and…
Crossing velocities for an annealed random walk in a random potential
Elena Kosygina, Thomas Mountford
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 t…
Limit laws of transient excited random walks on integers
Elena Kosygina, Thomas Mountford
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. Kos…
Lyapunov exponents of Green's functions for random potentials tending to zero
Elena Kosygina, Thomas S. Mountford, Martin P. W. Zerner
We consider quenched and annealed Lyapunov exponents for the Green's function of , where the potentials , are i.i.d. nonnegative random variables and i…
Positively and negatively excited random walks on integers, with branching processes
Elena Kosygina, Martin P. W. Zerner
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…