Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models
Bernoulli, cilt.24, sa.4B, ss.3283-3317, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 4B
- Basım Tarihi: 2018
- Doi Numarası: 10.3150/17-bej961
- Dergi Adı: Bernoulli
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3283-3317
- Anahtar Kelimeler: Concentration, Coupling, Log concave, Occupancy, Poisson Binomial distribution
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.