Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

George Deligiannidis; Zemer Kosloff

doi:10.1214/16-AOP1118

Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

George Deligiannidis, Zemer Kosloff

Research output: Contribution to journal › Article › peer-review

Abstract

We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.

Original language	English
Pages (from-to)	2505-2532
Number of pages	28
Journal	Annals of Probability
Volume	45
Issue number	4
DOIs	https://doi.org/10.1214/16-AOP1118
State	Published - 1 Jul 2017
Externally published	Yes

Keywords

Entropy
Fölner sequence
Random walk in random scenery
Relative complexity

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/16-AOP1118

Cite this

@article{f9e17a529b894898b426f1a7113ca308,

title = "Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times",

abstract = "We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the F{\"o}lner property almost surely.",

keywords = "Entropy, F{\"o}lner sequence, Random walk in random scenery, Relative complexity",

author = "George Deligiannidis and Zemer Kosloff",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2017.",

year = "2017",

month = jul,

day = "1",

doi = "10.1214/16-AOP1118",

language = "الإنجليزيّة",

volume = "45",

pages = "2505--2532",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "4",

}

TY - JOUR

T1 - Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

AU - Deligiannidis, George

AU - Kosloff, Zemer

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2017.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.

AB - We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.

KW - Entropy

KW - Fölner sequence

KW - Random walk in random scenery

KW - Relative complexity

UR - http://www.scopus.com/inward/record.url?scp=85027367032&partnerID=8YFLogxK

U2 - 10.1214/16-AOP1118

DO - 10.1214/16-AOP1118

M3 - مقالة

SN - 0091-1798

VL - 45

SP - 2505

EP - 2532

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this