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.