We provide a general bound on the Wasserstein distance between two arbitrary distributions
of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for …

We investigate increasing propagation of chaos for the mean-field Ising model of
ferromagnetism (also known as the Curie-Weiss model) with N spins at inverse temperature …

Compound Poisson approximation appears naturally in situations where one deals with a
large number of rare events. It has important applications in insurance, extreme value …

We prove a nonuniform local limit theorem concerning approximation of the point
probabilities P (S= k), where S=∑ i= 1 n X i, and X 1,…, X n are independent Bernoulli …

We investigate the local limit theorem for Poisson binomial random variables S< sub> n≔∑<
sub> i= 1< sup> n X< sub> i, where X< sub> 1, X< sub> 2,..., X< sub> n are independent …

We prove local limit theorems for mod-ϕ convergent sequences of random variables, ϕ
being a stable distribution. In particular, we give two new proofs of the local limit theorem …

In the seventies, Charles Stein revolutionized the way of proving the central limit theorem by
introducing a method that utilizes a characterization equation for Gaussian distribution. In …

In a recent paper the authors proved a nonuniform local limit theorem concerning normal
approximation of the point probabilities P (S= k) when S=∑ i= 1 n X i and X 1, X 2,…, X n are …

The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is
approximated by a multivariate compound Poisson distribution and by signed compound …

We study a multi-group version of the mean-field Ising model, also called Curie–Weiss
model. It is known that, in the high-temperature regime of this model, a central limit theorem …