Anatoly Vershik

Arithmetic, combinatorics and analysis of rational points on a cubic fourfold

We will consider a general unbounded additive problems from probabilistic and asymptotic point of view. There are two remarkable well-know examples of these problems --- one from combinatorics, to find the limit distribution of the partitions of the naturals indced by random permuations and the second from number theory, to find the limit distribution of logathms of prime divisors of the naturals.

Remarkable fact that asymtotics distribution in those very different probelms are the same and this is so called Poisson-Dirichlet (PD) distribution. There are no explantions of this coincideness. In theory of probability PD appeared as "Stack breaking process".

The new results concern to a Markov interpretation of PD-measure and to so called sigma-finite version of PD-measure, which has important connection with representation theory and mathematical physics ("Infinite-dimensional Lebesgue measure").