Saddle-point approximation in statistical physics, part I
Saddle-point approximation is more than an useful method for approximating an integral. In the first part of a two-part seminar, I will first review this method and then apply it to cheaply (i.e. without invoking heavy duty mathematics) derive some important results in statistics like the central limit theorem and large deviations principle. As a precursor to the second part, I will mention two cases when this method fails - nonequivalence of microcanonical and canonical ensembles in systems with long range interactions and condensation in one-dimensional mass transport models driven far from equilibrium.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..