| Título: | Scaling limits of recurrent excited random walks on integers |
| Autores: |
Dolgopyat, Dmitry; University of Maryland Kosygina, Elena; Baruch College and the CUNY Graduate Center |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
excited random walk; cookie walk; branching process; random environment; perturbed Brownian motion 60K37; 60F17; 60G50 |
| Descripción: | 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. |
| Idioma: | Inglés |
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