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Scaling limits of recurrent excited random walks on integers

   
@article{ECP2213,
	author = {Dmitry Dolgopyat and Elena Kosygina},
	title = {Scaling limits of recurrent excited random walks on integers},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {excited random walk; cookie walk; branching process; random environment; perturbed Brownian motion},
	abstract = {We describe scaling limits of recurrent excited random walks (ERWs) on $\mathbb{Z}$ in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations. It is known that ERW is recurrent if and only if the expected total drift per site, $\delta$, belongs to the interval $[-1,1]$. We show that if $|\delta|<1$ then the diffusively scaled ERW under the averaged measure converges to a $(\delta,-\delta)$-perturbed Brownian motion. In the boundary case, $|\delta|=1$, the space scaling has to be adjusted by an extra logarithmic term, and the weak limit of ERW happens to be a constant multiple of the running maximum of the standard Brownian motion, a transient process.},
	pages = {no. 35, 1-14},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-2213},    
        url = {http://ecp.ejpecp.org/article/view/2213}}