Flow Decomposition and Large Deviations

Quantitative Recurrence and Large Deviations for Teichmuller Geodesic Flow

We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on the moduli space Qg of holomorphic unit-area quadratic differentials on a compact genus g ≥ 2 surface.

Large Deviations

A Large Deviations Bound for the Teichmüller Flow

Largedeviation rates areobtained for suspension flows over symbolic dynamical systems with a countable alphabet. The method is that of [1]. A corollary of the main results is a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, which extends earlier work of J. Athreya [2]. The “entropy approach” we use is similar to that of [20] (see also [10], [13]).

Large Deviations

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example. Suppose that X random variables, for instance, normally distributed with mean zero and variance 1. Then, E e θ(X 1 +···+X n) = E[e θX ...

Large deviations for a stochastic model of heat flow

We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ− and τ+. Kipnis, Marchioro, and Presutti [18] proved that this model satisfies Fourier’s law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has...