# 11 березня 2021 року о 13 год 15 хв

A nested occupancy scheme in random environment is a generalization of the Karlin infinite balls-in-boxes occupancy scheme in random environment (with random probabilities). Unlike the Karlin scheme in which the collection of boxes is unique, there is a nested hierarchy of boxes, and the hitting probabilities of boxes are defined in terms of iterated fragmentation of a unit mass. We say that the boxes belong to the j-th level provided that their hitting probabilities are given by the j-fold fragmentation. Assuming that the number of balls is n, we shall present functional limit theorems for the number of occupied boxes in the j-th level in two different settings: 1) j is fixed; 2) j=j(n) diverges to infinity and j(n)=o((\log n)^{1/2}) as n tends to infinity.

Доповідач: **Alexander Iksanov**

Дата проведення: 11 березня 2021 року о 13 год 15 хв.