Further Advances in Nonconventional Limit Theorems

Yuri Kifer (Hebrew University Jerusalem)
Wednesday, July 1, 2015 - 6:00pm
TU Berlin, Raum MA041, Straße des 17. Juni 136, 10623 Berlin

Nonconventional limit theorems deal with the asymptotic behavior of sums of the form \sum_{n=1}^N F(\xi(q_1(n)), \xi(q_2(n)), ... \xi(q_l(n))) where F is a function, \xi(n); n \geq 0 is a stochastic process with some stationarity properties, in particular, it can be generated by a measure preserving transformation T in the form \xi(n) = f \circ T^n where f is a function. The functions q_j (n); j = 1,...,l take on nonnegative integer values on nonnegative integers and they satisfy some properties, for instance, they may have the form q_j(n) = jn. We discuss first the crucial question on positivity of the limiting variance for the sums above and then exhibit new results concerning the nonconventional local limit theorem, Berry-Esseen type estimates and the functional central limit theorem for the case when q_j(n)'s are general integer valued polynomials. These results are obtained together with my student Yeor Hafouta.