On the quenched functional CLT in random sceneries

Guy Cohen; Jean Pierre Conze

doi:10.4064/sm210421-13-10

On the quenched functional CLT in random sceneries

Guy Cohen, Jean Pierre Conze

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

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

Abstract

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Z^d-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random variables) and algebraic (when the r.f. is generated by commuting automorphisms of a torus or by commuting hyperbolic flows on homogeneous spaces).

Original language	American English
Pages (from-to)	261-303
Number of pages	43
Journal	Studia Mathematica
Volume	269
Issue number	3
DOIs	https://doi.org/10.4064/sm210421-13-10
State	Published - 1 Jan 2023

Keywords

S-unit
Z-action
cumulant
exponential mixing
flows on homogeneous spaces
quenched functional central limit theorem
random walk in random scenery
self-intersections of a random walk
toral automorphisms

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.4064/sm210421-13-10

Cite this

@article{1af5feb9cce144288b444d460e2aa8ac,

title = "On the quenched functional CLT in random sceneries",

abstract = "We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Zd-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random variables) and algebraic (when the r.f. is generated by commuting automorphisms of a torus or by commuting hyperbolic flows on homogeneous spaces).",

keywords = "S-unit, Z-action, cumulant, exponential mixing, flows on homogeneous spaces, quenched functional central limit theorem, random walk in random scenery, self-intersections of a random walk, toral automorphisms",

author = "Guy Cohen and Conze, {Jean Pierre}",

note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2023.",

year = "2023",

month = jan,

day = "1",

doi = "10.4064/sm210421-13-10",

language = "American English",

volume = "269",

pages = "261--303",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Instytut Matematyczny",

number = "3",

}

TY - JOUR

T1 - On the quenched functional CLT in random sceneries

AU - Cohen, Guy

AU - Conze, Jean Pierre

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2023.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Zd-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random variables) and algebraic (when the r.f. is generated by commuting automorphisms of a torus or by commuting hyperbolic flows on homogeneous spaces).

AB - We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Zd-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random variables) and algebraic (when the r.f. is generated by commuting automorphisms of a torus or by commuting hyperbolic flows on homogeneous spaces).

KW - S-unit

KW - Z-action

KW - cumulant

KW - exponential mixing

KW - flows on homogeneous spaces

KW - quenched functional central limit theorem

KW - random walk in random scenery

KW - self-intersections of a random walk

KW - toral automorphisms

UR - http://www.scopus.com/inward/record.url?scp=85161033311&partnerID=8YFLogxK

U2 - 10.4064/sm210421-13-10

DO - 10.4064/sm210421-13-10

M3 - Article

SN - 0039-3223

VL - 269

SP - 261

EP - 303

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

On the quenched functional CLT in random sceneries

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this