Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve

Alexander Iksanov; Alexander Marynych; Vladimir Vatutin

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arXiv · 1304.4469

Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve

Alexander Iksanov·Alexander Marynych·Vladimir Vatutin

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Abstract

The Bernoulli sieve is a random allocation scheme obtained by placing independent points with the uniform [0,1] law into the intervals made up by successive positions of a multiplicative random walk with factors taking values in the interval (0,1). Assuming that the number of points is equal to n we investigate the weak convergence, as n tends to infinity, of finite-dimensional distributions of the number of empty intervals within the occupancy range. A new argument enables us to relax the constraints imposed in previous papers on the distribution of the factor of the multiplicative random walk.

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Alexander Iksanov, Alexander Marynych, Vladimir Vatutin. 2013-04-16. Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve. https://arxiv.org/abs/1304.4469

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