Abstract:
Some classical and quantum spin systems (such as the Heisenberg models) are equivalent to probabilistic models of random loops. Looking at the lengths of the loops, we get measures on random partitions. It is conjectured that for quantum systems in dimensions 3 or greater, the measure on random partitions is always a Poisson-Dirichlet distribution.
I will explain what is known and what is expected in this context. I will also address the question of characterising random partition through “random colouring”. This is indirectly related to symmetries of the spin systems.
Biography:
Daniel Ueltschi is professor of mathematics at the University of Warwick (United Kingdom). He obtained his PhD in Theoretical Physics at the Ecole Polytechnique Federale of Lausanne (Switzerland) and subsequently held positions at Princeton, UC Davis, and Arizona, before moving to Warwick. His research deals with probabilistic approaches to condensed matter systems, and with various mathematical questions that arise from them. He is an expert of classical and quantum spin systems.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai