### Skapa referens, olika format (klipp och klistra)

**Harvard**

Blachere, S., den Hollander, F. och Steif, J. (2011) *A crossover for the bad configurations of random walk in random scenery*.

** BibTeX **

@article{

Blachere2011,

author={Blachere, S. and den Hollander, F. and Steif, Jeffrey},

title={A crossover for the bad configurations of random walk in random scenery},

journal={Annals of Probability},

issn={0091-1798},

volume={39},

issue={5},

pages={2018-2041},

abstract={In this paper, we consider a random walk and a random color scenery on Z. The increments of the walk and the colors of the scenery are assumed to be i.i.d. and to be independent of each other. We are interested in the random process of colors seen by the walk in the course of time. Bad configurations for this random process are the discontinuity points of the conditional probability distribution for the color seen at time zero given the colors seen at all later times. We focus on the case where the random walk has increments 0, +1 or -1 with probability epsilon, (1-epsilon)p and (1-epsilon)(1-p), respectively, with p is an element of [1/2, 1] and epsilon is an element of [0, 1), and where the scenery assigns the color black or white to the sites of Z with probability 1/2 each. We show that, remarkably, the set of bad configurations exhibits a crossover: for epsilon = 0 and p is an element of (1/2, 4/5) all configurations are bad, while for (p, epsilon) in an open neighborhood of (1, 0) all configurations are good. In addition, we show that for epsilon = 0 and p = 1/2 both bad and good configurations exist. We conjecture that for all epsilon is an element of [0, 1) the crossover value is unique and equals 4/5. Finally, we suggest an approach to handle the seemingly more difficult case where epsilon > 0 and p is an element of [1/2, 4/5), which will be pursued in future work.},

year={2011},

keywords={Random walk in random scenery, conditional probability distribution, bad, and good configurations, large deviations},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 149419

A1 Blachere, S.

A1 den Hollander, F.

A1 Steif, Jeffrey

T1 A crossover for the bad configurations of random walk in random scenery

YR 2011

JF Annals of Probability

SN 0091-1798

VO 39

IS 5

SP 2018

OP 2041

AB In this paper, we consider a random walk and a random color scenery on Z. The increments of the walk and the colors of the scenery are assumed to be i.i.d. and to be independent of each other. We are interested in the random process of colors seen by the walk in the course of time. Bad configurations for this random process are the discontinuity points of the conditional probability distribution for the color seen at time zero given the colors seen at all later times. We focus on the case where the random walk has increments 0, +1 or -1 with probability epsilon, (1-epsilon)p and (1-epsilon)(1-p), respectively, with p is an element of [1/2, 1] and epsilon is an element of [0, 1), and where the scenery assigns the color black or white to the sites of Z with probability 1/2 each. We show that, remarkably, the set of bad configurations exhibits a crossover: for epsilon = 0 and p is an element of (1/2, 4/5) all configurations are bad, while for (p, epsilon) in an open neighborhood of (1, 0) all configurations are good. In addition, we show that for epsilon = 0 and p = 1/2 both bad and good configurations exist. We conjecture that for all epsilon is an element of [0, 1) the crossover value is unique and equals 4/5. Finally, we suggest an approach to handle the seemingly more difficult case where epsilon > 0 and p is an element of [1/2, 4/5), which will be pursued in future work.

LA eng

DO 10.1214/11-aop664

LK http://dx.doi.org/10.1214/11-aop664

LK http://publications.lib.chalmers.se/records/fulltext/local_149419.pdf

OL 30