Lectures on large deviations in probability and dynamical systems

2015 ◽  
pp. 45-79
Author(s):  
Yuri Kifer
Keyword(s):  
Dynamical Systems ◽  
Large Deviations

scholarly journals A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

2010 ◽  
Vol 31 (4) ◽  
pp. 1043-1071 ◽  
Author(s):  
VÍTOR ARAÚJO ◽  
ALEXANDER I. BUFETOV
Keyword(s):  
Dynamical Systems ◽  
Large Deviations ◽  
Moduli Space ◽  
Geodesic Flow ◽  
Large Deviation ◽  
Suspension Flows ◽  
Abelian Differentials ◽  
Quantitative Recurrence ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Flow

AbstractLarge deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

scholarly journals Weak specification properties and large deviations for non-additive potentials

2013 ◽  
Vol 35 (3) ◽  
pp. 968-993 ◽  
Author(s):  
PAULO VARANDAS ◽  
YUN ZHAO
Keyword(s):  
Dynamical Systems ◽  
Large Deviations ◽  
Lyapunov Exponents ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Deviation Principle ◽  
Hyperbolic Dynamical Systems

AbstractWe obtain large deviation bounds for the measure of deviation sets associated with asymptotically additive and sub-additive potentials under some weak specification properties. In particular, a large deviation principle is obtained in the case of uniformly hyperbolic dynamical systems. Some applications to the study of the convergence of Lyapunov exponents are given.

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