## Bernoulli

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

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

#### 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
Revised: May 2017
First available in Project Euclid: 18 April 2018

https://projecteuclid.org/euclid.bj/1524038755

Digital Object Identifier
doi:10.3150/17-BEJ961

Mathematical Reviews number (MathSciNet)
MR3788174

Zentralblatt MATH identifier
06869877

#### 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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