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Quantum spanning forests

Presented by: 
Adrien Kassel ENS - Lyon, CNRS (Centre national de la recherche scientifique)
Date: 
Thursday 19th July 2018 - 14:35 to 15:20
Venue: 
INI Seminar Room 1
Abstract: 
I will introduce a new integrable statistical physics model, which we call a quantum spanning forest (QSF) and which provides a probabilistic framework for studying spanning-tree like structures coupled to a connection (with holonomies taking values in a unitary group of arbritrary rank), both on finite and infinite graphs. I will explain that QSFs form a special case of a new general family of probability measures which we call determinantal subspace processes (DSP), and for which we develop an independent theory. Finally, I will describe some relationships between QSFs and holonomies of random walk and the covariant Gaussian free field via the study of electrical networks with holonomy. This is joint work with Thierry Lévy.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons