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

2 Scopus citations

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

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2017.

Keywords

Entropy
Fölner sequence
Random walk in random scenery
Relative complexity

Access to Document

10.1214/16-AOP1118

Cite this

@article{564e7051e2bb43a49d8062ebfbd3b7fc,

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 = "אנגלית",

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 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85027367032

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

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this