This survey article discusses the main concepts and techniques of Stein's method for
distributional approximation by the normal, Poisson, exponential, and geometric …

Coalescent theory is the study of random processes where particles may join each other to
form clusters as time evolves. These notes provide an introduction to some aspects of the …

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

Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour
(July 7–24, 2002), by the Professors Pitman, Tsirelson and Werner …

Our basic question is: Given a collection of DNA sequences, what underlying forces are
responsible for the observed patterns of variability? To approach this question we introduce …

This paper has two parts. The first part surveys Euler's work on the constant $\gamma=
0.57721\cdots $ bearing his name, together with some of his related work on the gamma …

These lecture notes are intended to be used for master courses, where the students have a
limited prior knowledge of special topics in probability. Therefore, we have included many of …

We give a unified treatment of the limit, as the size tends to infinity, of random simply
generated trees, including both the well-known result in the standard case of critical Galton …

Ewens's sampling formula exemplifies the harmony of mathematical theory, statistical
application, and scientific discovery. The formula not only contributes to the foundations of …

The paper deals with the problem of determining the number of components in a mixture
model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a …