Annealed deviations of random walk in random scenery
| dc.creator | Gantert, Nina | |
| dc.creator | König, Wolfgang | |
| dc.creator | Shi, Zhan | |
| dc.date | 2004-08-24 | |
| dc.date | 2005-11-21 | |
| dc.date.accessioned | 2026-07-07T06:38:45Z | |
| dc.date.available | 2026-07-07T06:38:45Z | |
| dc.description | Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d. scenery, independent of the walk. The walker's steps have mean zero and finite variance. We identify the speed and the rate of the logarithmic decay of $¶(\frac 1n Z_n>b_n)$ for various choices of sequences $(b_n)_n$ in $[1,\infty)$. Depending on $(b_n)_n$ and the upper tails of the scenery, we identify different regimes for the speed of decay and different variational formulas for the rate functions. In contrast to recent work \cite{AC02} by A. Asselah and F. Castell, we consider sceneries {\it unbounded} to infinity. It turns out that there are interesting connections to large deviation properties of self-intersections of the walk, which have been studied recently by X. Chen \cite{C03}. | |
| dc.description | 32 pages, revised | |
| dc.identifier | https://arxiv.org/abs/math/0408327 | |
| dc.identifier | http://arxiv.org/abs/math/0408327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100847 | |
| dc.subject | Probability | |
| dc.subject | 60K37, 60F10, 60J55 | |
| dc.title | Annealed deviations of random walk in random scenery | |
| dc.type | text |