Bernoulli

  • Bernoulli
  • Volume 24, Number 4B (2018), 3283-3317.

Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models

Jay Bartroff, Larry Goldstein, and Ümit Işlak

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Abstract

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.

Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3283-3317.

Dates
Received: December 2016
Revised: May 2017
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1524038755

Digital Object Identifier
doi:10.3150/17-BEJ961

Mathematical Reviews number (MathSciNet)
MR3788174

Zentralblatt MATH identifier
06869877

Keywords
concentration coupling log concave occupancy Poisson Binomial distribution

Citation

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


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