Metastability and related phenomena are associated to systems "trapped" for a long time in some part of their phase space, from which they emerge in a random time ---the exit time--- expected to have an asymptotic exponential distribution. These phenomena are the subject of many current studies in the mathematical literature. I will overview the scope and limitations of different approaches and will focus in the one closest to physical intuition: the pathwise approach. I will present a general theory recently developed with F. Manzo, F. Nardi, E. Scoppola and J. Sohier which applies for general metastability mechanisms. A particularity of the theory is that it considers metastable states as full fledged probability measures whose proper definition will be discussed.
Biography
Roberto Fernández is a Chair Professor in Stochastics at Utrecht University. His main research is mathematical statistical mechanics (classical and quantum). In this field Professor Fernandez has worked on rigorous determination of critical exponents, non-Gibbs phenomena, uniqueness criteria, convergence of cluster expansions and quantum phase diagrams. He has also works in the theory of stochastic processes, with emphasis in chains with long memory. Other topics include perfect simulation algorithms, cutoff and escape behavior in Markov processes and applications of stochastic processes to biological processes and language acquisition.