Duality and symmetry in interacting particle systems
Duality is an important concept in the study of stochastic interacting particle systems. For arbitrary initial measures duality expresses expectations of a family of functions at time $t$ in terms of the transition probability of a dual process which may be simpler to analyse. Focussing on countable state space we discuss duality from the perspective of the generator. Unlike the more traditional approach of looking at duality in a pathwise manner this allows us to understand straightforwardly how dualities arise from symmetries, or more generally, from invariant subspaces of the generator and leads to constructive methods for finding useful dualities. Also the new concept of reverse duality comes out naturally. It yields the full probability measure of the process at time $t$ for a family of initial measures in terms of transition probabilities of the dual process and thus allows for the computation of arbitrary expectation values.
13:00– Europe/Lisbon Unusual schedule
Room P3.10, Mathematics Building Instituto Superior Técnico
— Online
From Statistical Mechanics to Quantum Mechanics, Quantum Field Theory or even Hydrodynamics, Probability has progressively become a fundamental toolbox in Mathematical Physics, unifying methods of research in domains that were regarded as separate for a long time. This series of seminars aims to showcase bridges between such domains, including those too recent to be regarded as associated with Theoretical or Mathematical Physics.
