Gaussian Fluctuations in Determinantal Random Point
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.