Suppose we are given a multiplicative random walk (a

stick-breaking set) generated by a random variable W taking values in the

interval (0,1) and a sample from the uniform [0,1] law which is

independent of the stick-breaking set. The Bernoulli sieve is a random

occupancy scheme in which 'balls' represented by the points of the uniform

sample are allocated over an infinite array of 'boxes' represented by the

gaps in the stick-breaking set. Assuming that the number of balls equals n

I am interested in the weak convergence of the number of empty boxes

within the occupancy range as n approaches infinity. Depending on the

behavior of the law of W near the endpoints 0 and 1 the number of empty

boxes can exhibit quite a wide range of different asymptotics. I will

discuss the most interesting cases with an emphasis on the methods

exploited.

# Asymptotics of the number of empty boxes in the Bernoulli sieve

Speaker:

Alexander Iksanov (National T. Shevchenko University, Kiev)

Date/Time:

Wed, 20/03/2013 - 16:00

Room:

M203

Seminar series: