Gaussian asymptotics of discrete $\beta $ -ensembles - ENS de Lyon - École normale supérieure de Lyon Access content directly
Journal Articles Publications Mathématiques de L'IHÉS Year : 2017

Gaussian asymptotics of discrete $\beta $ -ensembles


We introduce and study stochastic N –particle ensembles which are discretizations for general–β log-gases of random matrix theory. The examples include random tilings, families of non–intersecting paths, (z, w)–measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as N → ∞. The covariance is universal and coincides with its counterpart in random matrix theory. Our main tool is an appropriate discrete version of the Schwinger–Dyson (or loop) equations, which originates in the work of Nekrasov and his collaborators.
Fichier principal
Vignette du fichier
Discrete_Loop9.pdf (816.8 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

ensl-01400956 , version 1 (22-11-2016)



Alexei Borodin, Vadim Gorin, Alice Guionnet. Gaussian asymptotics of discrete $\beta $ -ensembles. Publications Mathématiques de L'IHÉS, 2017, 125, pp.1--78. ⟨10.1007/s10240-016-0085-5⟩. ⟨ensl-01400956⟩
78 View
83 Download



Gmail Facebook Twitter LinkedIn More