Journal article
Local limit theorems for occupancy models
AD Barbour, Peter Braunsteins, Nathan Ross
RANDOM STRUCTURES & ALGORITHMS | WILEY | Published : 2020
DOI: 10.1002/rsa.20967
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 neighbors in a germ‐grain model, and the number of degree‐d vertices in an Erdős‐Rényi random graph. In both cases, the error rate is optimal, up to logarithmic factors.
Related Projects (2)
Grants
Awarded by Australian Research Council (ARC)
Awarded by ARC Centre of Excellence for Mathematical and Statistical Frontiers
Funding Acknowledgements
This research was supported by the Australian Research Council (ARC) Grant, DP150101459. FL130100039. ARC Centre of Excellence for Mathematical and Statistical Frontiers, CE140100049.