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• W2965622170 abstract "We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random variables. The method is applicable when a Stein coupling can be exhibited. Our approach involves both Stein's method for distributional approximation and Stein's method for concentration. As applications, we prove local central limit theorems with rate of convergence for the number of germs with $d$ neighbours in a germ--grain model, and the number of degree-$d$ vertices in an ErdH{o}s--R'enyi random graph. In both cases, the error rate is optimal, up to logarithmic factors." @default.
• W2965622170 created "2019-08-13" @default.
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• W2965622170 date "2019-08-01" @default.
• W2965622170 modified "2023-09-24" @default.
• W2965622170 title "Local limit theorems for occupancy models" @default.
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• W2965622170 doi "https://doi.org/10.48550/arxiv.1908.00251" @default.
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