Professor Takis Konstantopoulos will talk about the relations between random matrices, their eigenvalues, and the queueing models, such as M/M/1 queues in series.
Recently, connections with random graphs were found and some approximation results that lead to the Tracy-Widom distribution will be explained.
Professor Sergey Zuev will present a course on Point processes and Poisson random measures that will cover:
- Introduction to point processes (fields) in general spaces, moment measures, probability generating functional and Laplace functional, Fock space, cluster processes, infinitely divisible processes, Campbell theorem and Palm distribution;
- Construction of general Poisson processes and their main properties: superposition, thinning, point translation, Mecke-Slivnyak characterisation;
- Advanced properties of Poisson random measures: variation analysis, chaos decomposition, covariance identities and log-Sobolev inequalities;
- Clark-Okone martingale representation for Poisson martingales, Stein’s method and normal approximation of Poisson functionals, some applications to stochastic geometry and statistics.
Novosibirsk State University
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk