Speaker
Alice Guionnet
Description
Discrete Theta-ensembles generalize the distribution of random
tiling in the same way that beta-ensembles generalize that of Gaussian
matrices. Non-intersecting Bernoulli random walks generalize Dyson
Brownian motion to the discrete ensemble. In this talk, I will discuss
large deviations for these objects, with applications to study the
asymptotics of Jack and Mac Donald polynomials. The techniques are based
on the analysis of the so-called Nekrasov's equations which are discrete
analogues of the loop or Dyson-Schwinger's equations. It generalizes to
the discrete setting the large deviations for the Dyson Brownian motion
derived by G-Zeitouni, see also G-Huang. This talk is based on a recent
joint Jiaoyang Huang.