Lectures on Probability Theory and Statistics Ecole d'Eté de Probabilités de Saint-Flour XXX - 2000

Sergio Albeverio: Theory of Dirichlet forms and applications.- Functional analytic background: semigroups, generators, resolvents.- Closed symmetric coercive forms associated with Co-contraction semigroups.- Contraction properties of forms, positivity preserving and submarkovian semigroups.- Potential Theory and Markov Processes associated with Dirichlet Forms.- Diffusions and stochastic differential equations associated with classical Dirichlet forms.- Applications.- Walter Schachermayer: Introduction to the Mathematics of Financial Markets.- Introduction: Bachelier’s Thesis from 1900.- Models of Financial Markets on Finite Probability Spaces.- The Binomial Model, Bachelier’s Model and the Black-Scholes Model.- The No-Arbitrage Theory for General Processes.- Some Applications of the Fundamental Theorem of Asset Pricing.- Michel Talagrand: Mean field models for spin glasses: a first course.- What this is all about: the REM.- The Sherrington-Kirkpatrick model at high temperature.- The p-spin interaction model.- External field and the replica-symmetric solution.- Exponential inequalities.- Central limit theorems and the Almeida-Thouless line.- Emergence and separation of the lumps in the p-spin interaction model.