- Volume 24, Number 4B (2018), 3283-3317.
Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models
Threshold-type counts based on multivariate occupancy models with log concave marginals admit bounded size biased couplings under weak conditions, leading to new concentration of measure results for random graphs, germ-grain models in stochastic geometry and multinomial allocation models. The results obtained compare favorably with classical methods, including the use of McDiarmid’s inequality, negative association, and self bounding functions.
Bernoulli, Volume 24, Number 4B (2018), 3283-3317.
Received: December 2016
Revised: May 2017
First available in Project Euclid: 18 April 2018
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Bartroff, Jay; Goldstein, Larry; Işlak, Ümit. Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models. Bernoulli 24 (2018), no. 4B, 3283--3317. doi:10.3150/17-BEJ961. https://projecteuclid.org/euclid.bj/1524038755