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A quenched functional central limit theorem for planar random walks in random sceneries

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1.	Title	Title of document	A quenched functional central limit theorem for planar random walks in random sceneries
2.	Creator	Author's name, affiliation, country	Nadine Guillotin-Plantard; Université Lyon 1; France
2.	Creator	Author's name, affiliation, country	Julien Poisat; Leiden Universiteit; Netherlands
2.	Creator	Author's name, affiliation, country	Renato Soares dos Santos; Université Lyon 1; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random walk in random scenery; Limit theorem; Local time; Associated Random Variables
3.	Subject	Subject classification	60F05, 60G52
4.	Description	Abstract	Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes with stationary increments. Two sources of randomness enter in their definition: a random field $\xi = (\xi(x))_{x \in \mathbb{Z}^d}$ of i.i.d. random variables, which is called the random scenery, and a random walk $S = (S_n)_{n \in \mathbb{N}}$ evolving in $\mathbb{Z}^d$, independent of the scenery. The RWRS $Z = (Z_n)_{n \in \mathbb{N}}$ is then defined as the accumulated scenery along the trajectory of the random walk, i.e., $Z_n := \sum_{k=1}^n \xi(S_k)$. The law of $Z$ under the joint law of $\xi$ and $S$ is called "annealed'', and the conditional law given $\xi$ is called "quenched''. Recently, functional central limit theorems under the quenched law were proved for $Z$ by the first two authors for a class of transient random walks including walks with finite variance in dimension $d \ge 3$. In this paper we extend their results to dimension $d=2$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR project MEMEMO2 10--BLAN--0125--03 and ERC Advanced Grant 267356 VARIS
7.	Date	(YYYY-MM-DD)	2014-01-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/3002
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-3002
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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