### Abstract

We consider the (d +1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on ℤ^{d} together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this dynamical system. The proofs are direct: we do not use the coding constructed by Jiang [Preprint (2002)] for such systems.

Original language | English (US) |
---|---|

Pages (from-to) | 692-729 |

Number of pages | 38 |

Journal | Annals of Probability |

Volume | 32 |

Issue number | 1 B |

State | Published - Jan 2004 |

### Fingerprint

### Keywords

- Coupled map lattices
- Large deviations
- Thermodynamic formalism

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Probability*,

*32*(1 B), 692-729.

**Spatio-temporal large deviations principle for coupled circle maps.** / Bardet, Jean Baptiste; Arous, Gérard Ben.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 32, no. 1 B, pp. 692-729.

}

TY - JOUR

T1 - Spatio-temporal large deviations principle for coupled circle maps

AU - Bardet, Jean Baptiste

AU - Arous, Gérard Ben

PY - 2004/1

Y1 - 2004/1

N2 - We consider the (d +1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on ℤd together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this dynamical system. The proofs are direct: we do not use the coding constructed by Jiang [Preprint (2002)] for such systems.

AB - We consider the (d +1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on ℤd together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this dynamical system. The proofs are direct: we do not use the coding constructed by Jiang [Preprint (2002)] for such systems.

KW - Coupled map lattices

KW - Large deviations

KW - Thermodynamic formalism

UR - http://www.scopus.com/inward/record.url?scp=2142640520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142640520&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 692

EP - 729

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 1 B

ER -