
 Professor
 Frank Redig
 TU Delft
 Probability Theory
Duality and exactly solvable models in nonequilibrium
The aim of the talk is to give a simple introduction in the theory of duality of Markov processes, and its applications in statistical physics. In statistical physics, one is interested in understanding how the macro world emerges from the micro world. In nonequilibrium systems, such as a metal rod in contact with two different temperatures, there is no analogue of the BoltzmannGibbs distribution, and the study of such systems relies on simplified models called ``interacting particle systems’’. Some of these models have extra symmetries which implies that we can obtain closed form formulas for quantities of relevance such as the temperature profile, and correlation functions. The key to solve these special systems is ``duality’’. Duality is a way to connect two Markov processes via a socalled duality function. Finding dual processes, and the corresponding duality functions is intimately related to finding symmetries of Markov processes, which in turn connects Markov process theory with Lie theory. In this sense, such special systems enjoying duality come in ``groups’’ associated to Lie algebras. I will describe how these processes are built for the Lie algebras SU(2) (exclusion processes) and SU(1,1) (inclusion processes).
About
Short CV:
1992: PhD Universiteit Antwerpen (cum laude)
19982000: Postdoc Katholieke Universiteit Leuven
20002005: Assistant professor, Technische Universiteit Eindhoven
20052010: Associate professor, Universiteit Leiden
20102011: Full professor of applied probability Radboud University Nijmegen
Since 2011: : Full professor of applied probability Technical University of Delft
Research interests:
Markov processes, interacting particle systems, nonequilibrium statistical physics, selforganized criticality and sandpile models, large deviations, concentration inequalities, random walk.
Redig's Homepage