scholarly journals Large deviation principles for Langevin equations in random environment and applications

2021 ◽  
Vol 62 (8) ◽  
pp. 083301
Author(s):  
Nhu N. Nguyen ◽  
George Yin
Keyword(s):  
Random Environment ◽  
Large Deviation ◽  
Langevin Equations ◽  
Large Deviation Principles

scholarly journals Large deviations in non-uniformly hyperbolic dynamical systems

2008 ◽  
Vol 28 (2) ◽  
pp. 587-612 ◽  
Author(s):  
LUC REY-BELLET ◽  
LAI-SANG YOUNG
Keyword(s):  
Dynamical Systems ◽  
Generating Functions ◽  
Limit Theorems ◽  
Large Deviation ◽  
Return Times ◽  
Hyperbolic Diffeomorphisms ◽  
Large Deviation Principles ◽  
Hyperbolic Dynamical Systems ◽  
Rank One ◽  
Dispersing Billiards

AbstractWe prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hénon-type attractors.

scholarly journals Large deviations and fluctuation theorem for selectively decoupled measures on shift spaces

2019 ◽  
Vol 31 (10) ◽  
pp. 1950036 ◽  
Author(s):  
Noé Cuneo ◽  
Vojkan Jakšić ◽  
Claude-Alain Pillet ◽  
Armen Shirikyan
Keyword(s):  
Multifractal Analysis ◽  
Invariant Measures ◽  
Large Deviation ◽  
Thermodynamic Formalism ◽  
Hard Core ◽  
Shift Spaces ◽  
Large Deviation Principles ◽  
Fluctuation Relation ◽  
Level 3 ◽  
Level 1

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained.

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