• Professor
    • Frank Redig
    • TU Delft
    • Probability Theory

Duality and exactly solvable models in non-equilibrium

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 non-equilibrium systems, such as a metal rod in contact with two different temperatures, there is no analogue of the Boltzmann-Gibbs 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 so-called 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)

1998-2000: Postdoc Katholieke Universiteit Leuven

2000-2005: Assistant professor, Technische Universiteit Eindhoven

2005-2010: Associate professor, Universiteit Leiden

2010-2011: 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, non-equilibrium statistical physics, self-organized criticality and sandpile models, large deviations, concentration inequalities, random walk.

Redig's Homepage