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QUENCHED LIMIT THEOREMS FOR RANDOM U(1) EXTENSIONS OF EXPANDING MAPS

Chung, Yong Moo ; Nakano, Yushi LU and Wittsten, Jens LU (2023) In Discrete and Continuous Dynamical Systems- Series A 43(1). p.338-377
Abstract

In this paper we provide quenched central limit theorems, large deviation principles and local central limit theorems for random U(1) extensions of expanding maps on the torus. The results are obtained as special cases of corresponding theorems that we establish for abstract random dynamical systems. We do so by extending a recent spectral approach developed for quenched limit theorems for expanding and hyperbolic maps to be applicable also to partially hyperbolic dynamics.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Central limit theorem, Lyapunov spectrum, partially hyperbolic map, random dynamical system, transfer operator
in
Discrete and Continuous Dynamical Systems- Series A
volume
43
issue
1
pages
40 pages
publisher
American Institute of Mathematical Sciences
external identifiers
  • scopus:85143638986
ISSN
1078-0947
DOI
10.3934/dcds.2022151
language
English
LU publication?
yes
id
d7f4578e-0c0c-4bf1-8b13-ae2ad1815924
date added to LUP
2023-02-07 15:08:28
date last changed
2023-02-07 15:08:28
@article{d7f4578e-0c0c-4bf1-8b13-ae2ad1815924,
  abstract     = {{<p>In this paper we provide quenched central limit theorems, large deviation principles and local central limit theorems for random U(1) extensions of expanding maps on the torus. The results are obtained as special cases of corresponding theorems that we establish for abstract random dynamical systems. We do so by extending a recent spectral approach developed for quenched limit theorems for expanding and hyperbolic maps to be applicable also to partially hyperbolic dynamics.</p>}},
  author       = {{Chung, Yong Moo and Nakano, Yushi and Wittsten, Jens}},
  issn         = {{1078-0947}},
  keywords     = {{Central limit theorem; Lyapunov spectrum; partially hyperbolic map; random dynamical system; transfer operator}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{338--377}},
  publisher    = {{American Institute of Mathematical Sciences}},
  series       = {{Discrete and Continuous Dynamical Systems- Series A}},
  title        = {{QUENCHED LIMIT THEOREMS FOR RANDOM U(1) EXTENSIONS OF EXPANDING MAPS}},
  url          = {{http://dx.doi.org/10.3934/dcds.2022151}},
  doi          = {{10.3934/dcds.2022151}},
  volume       = {{43}},
  year         = {{2023}},
}