Beta Ensembles: Universality, Integrability, and Asymptotics (16w5076)


(Temple University)

Peter Forrester (University of Melbourne)

Alice Guionnet (Massachusetts Institute of Technology)

(University of Wisconsin - Madison)


The Banff International Research Station will host the "Beta Ensembles: Universality, Integrability, and Asymptotics" workshop from April 10th to April 15th, 2016.

Random matrix theory is a vibrant area of probability theory and mathematical physics, with applications across mathematics, physics and engineering.
Starting with the work of Dyson, Gaudin and Mehta in the 60s and 70s and then with the ground breaking results of Tracy and Widom in the 90s (building on the work of the Kyoto group in the 80s) the classical “invariant” ensembles of random matrix theory turned out to be exactly solvable. In particular, the local behavior of the eigenvalues of these ensembles has been fully described. Moreover, many of the limiting objects were soon after understood to capture the scaling limits of other integrable systems from combinatorics and statistical physics, most famously of various models of random growth composing the KPZ universality class.

The physically motivated beta-ensembles (which can initially be viewed as a models of a coulomb gas) provide one-parameter families of particle systems that interpolate between the eigenvalue distributions of several of the classical models (realized at beta equal to 1, 2, or 4). In recent years, the introduction of a range of new tools led to a period of intense research activity on the general beta ensembles, and our understanding of their properties continues at a fast pace. The wide range of new results naturally raise many open problems. This workshop will bring together various groups, in probability, mathematical physics, and numerical analysis, working on the theory of beta-ensembles to discuss the most recent results and open problems in the field.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides
an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional
de Ciencia y Tecnología (CONACYT).