Luc Rey-Bellet (U. of Massachusetts, Amherst, USA)
 
Large deviations for Gibbs states and Markov chains (mp_arc/04-199)


This course is a short introduction to the theory of large deviations. We will start with two basic results: Cramer's Theorem for for sum of i.i.d random and Gartner-Ellis Theorem for sequences of dependent random variables. As an application we will discuss large deviations for Markov chains under various assumptions (compact and non-compact state space). Next we will discuss the Gibbs states of classical and quantum spin systems and the natural relations between large deviations and the thermodynamic formalism. if time permits we will also discuss large deviation properties in dynamical systems.