CIMPA School: Mar del Plata 2012

Probability is an area of mathematics that has experienced tremendous progress in the last few decades. It models uncertainty in terms of random variables and processes and develops techniques to study random dynamical systems. Stochastic processes have become a standard modelling tool in most scientific areas and the source of novel simulation and combinatorial algorithms of surprising efficiency (Monte Carlo, perfect simulations, stochastic integration,...).
Their analysis finds particular relevance and resonance when applied to statistical physics and information systems. In both cases, the size of the systems, the complexity of the underlying dynamics and the randomness of the environment or traffic prevent the use of straightforward deterministic computational methods or simulations. While there are many similarities in the methodologies employed in queuing theory and in the study of interacting particles systems, there are not always clear bridges between the two areas. A specific focus will be given to create and consolidate links between the two research avenues.

In more technical terms, the school is expected to focus on probabilistic problems like multi-scale metastable behaviors, perfect simulation of random systems, dynamical Gibbs-nonGibbs transitions, perturbative treatment of systems at extreme temperature, fluid and hydrodynamic limits for large scale systems and stochastic stability analysis. Particular attention will be given throughout the course to explaining in detail specific techniques to attack these problems like coupling and duality methods, martingale and scaling techniques, Palm probabilities and stochastic geometry.