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

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	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

ASJC Scopus subject areas

General Mathematics

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KW - S-unit

KW - Z-action

KW - cumulant

KW - exponential mixing

KW - flows on homogeneous spaces

KW - quenched functional central limit theorem

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KW - self-intersections of a random walk

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On the quenched functional CLT in random sceneries

Abstract

Keywords

ASJC Scopus subject areas

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