Alexander Soshnikov, Caltech, U.S.A.

Gaussian Fluctuations in Determinantal Random Point Fields


  Determinantal random point fields (processes) are random point fields such that k-point correlation functions are the determinants of k by k matrices with an integral kernel. Such point processes appear in many areas of mathematics and mathematical physics, including Random Matrix Theory, Representation Theory, Quantum Mechanics, Statistical Mechanics, Probability Theory. Very often the kernel can be expressed in terms of special functions (thus Airy, Bessel, hypergeometric etc random point fields).
   In the talk we give the examples of determinantal random point fields and discuss the Central Limit Theorem for the linear statistics.

Recent preprints: