Prof. M.Bertola seminar

[Boris Dubrovin]

Seminar announcement

Title: Determinantal random point fields, gap probabilities and the  
Riemann--Hilbert approach

Speaker: Prof. Marco Bertola (Concordia University, Montreal)

Date: Wednesday, April 17, 2013, 14:00-15:00

Room: SISSA Main Building, room 136


Abstract: I will start by reviewing the notion of (determinantal)  
random point fields.
Famous examples of their beautiful applications are:
1) the eigenvalues of certain type of random matrices;
2) mutually avoiding one-dimensional Brownian motions (Dyson  
process, ) and certain limits thereof;
3) the Frobenius coordinates of Young Diagrams associated to the   
Poissonized Plancherel measure on the set of representations of the  
permutation groups.

The expectations of occupation numbers of subsets of the configuration  
space can be expressed as Fredholm (infinite dimensional)  
determinants, the evaluation of which leads very often to a Riemann-- 
Hilbert problem (a notion that I will review briefly).
This in turns allows to connect these probabilities to the ever- 
expanding area of Painlevé  like equations and isomonodromic  
deformations.
I will try to touch upon these topics and review some results of my  
collaborators and myself.