@article{EJP2940,
author = {Elena Kosygina and Martin Zerner},
title = {Excursions of excited random walks on integers},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {branching process, cookie walk, diffusion approximation, excited random walk, excursion, squared Bessel process, return time, strong transience},
abstract = {Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter $\delta\in\mathbb R$. For recurrence/transience the critical threshold is $|\delta|=1$, for ballisticity it is $|\delta|=2$ and for diffusivity $|\delta|=4$. In this paper we establish a phase transition at $|\delta|=3$. We show that the expected return time of the walker to the starting point, conditioned on return, is finite iff $|\delta|>3$. This result follows from an explicit description of the tail behaviour of the return time as a function of $\delta$, which is achieved by diffusion approximation of related branching processes by squared Bessel processes.},
pages = {no. 25, 1-25},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2940},
url = {http://ejp.ejpecp.org/article/view/2940}}