Integrable Systems Seminar

[Boris Dubrovin]

Dear All,

Next meeting of the Integrable Systems Seminar will take place on

Wednesday, October 26 at 14:00 - 15:30 (note unusual time!), room 133
of SISSA Main Building

Speaker: Prof. T.Grava (SISSA)

Title: From Random Matrices to Stochastic operators and beta-Tracy-Widom distribution

Abstract: I will   consider a  Coulomb gas at inverse temperature beta.
Such model can be reduced to a matrix model known as beta ensemble.  Fluctuations of statistical quantities can be  described by stochastic differential operators.
I will focus on the largest eigenvalue distribution of the beta-ensemble. Such distribution is described  
by the largest eigenvalue of the  stochastic Airy operator.  The connection of such operator with the   beta-Tracy-Widom distribution and  the Painleve’ II equation will be explained.

References: Edelman and Sutton, From Random Matrices to Stochastic operators, 
		    Journal of Statistical Physics 2007.
                  
		    J.Ramirez, B. Rider, B. Virag,   Beta ensemble, stochastic Airy spectrum and diffusion, 
		    Journal of the  American Mathematical Society 2011

Boris Dubrovin