Analytic combinatorics aims to enable precise quantitative predictions of the properties of
large combinatorial structures. The theory has emerged over recent decades as essential …

This book explains similarities in asymptotic behavior as the result of two basic properties
shared by the structures: the conditioning relation and the logarithmic condition. The …

Since the birth of probability theory, weak convergence has played a major role in the field.
One of the most celebrated examples of weak convergence is the central limit theorem. If (Yi) …

We obtain a central limit theorem for a general class of additive parameters (costs,
observables) associated to three standard Euclidean algorithms, with optimal speed of …

This article describes a purely analytic approach to urn models of the generalized or
extended Pólya–Eggenberger type, in the case of two types of balls and constant “balance,” …

Given a multivariate generating function F (z1,…, zd)=∑ ar1,…, rdzr11… zrdd, we determine
asymptotics for the coefficients. Our approach is to use Cauchy's integral formula near …

Stirling permutations were introduced by Gessel and Stanley in 1978, who enumerated them
by the number of descents to give a combinatorial interpretation of certain polynomials …

The survey is dedicated to a celebrated series of quantitave results, developed by the
Lithuanian school of probability, on the normal approximation for a real-valued random …

We prove a general central limit theorem for probabilities of large deviations for sequences
of random variables satisfying certain analytic conditions. This theorem has wide …

We study linear recurrences of Eulerian type of the form P n (v)=(α (v) n+ γ (v)) P n− 1 (v)+ β
(v)(1− v) P n− 1′(v)(n⩾ 1), with P 0 (v) given, where α (v), β (v) and γ (v) are in most cases …