Incorporating a collection of recent results, Polya Urn Models deals with discrete probability
through the modern and evolving urn theory and its numerous applications. It looks at how …

This paper surveys some key developments that have occurred pertaining to urn models in
probabilistic, statistical and biological literatures during the past two decades. It should be …

A functional limit theorem is proved for multitype continuous time Markov branching
processes. As consequences, we obtain limit theorems for the branching process stopped …

Consider some model of random finite trees of increasing size. It often happens that the
subtree at a uniform random vertex converges in distribution to a limit random tree. We …

We investigate a very simple model describing the evolution of protein-protein interaction
networks via duplication and divergence. The model exhibits a remarkably rich behavior …

We propose a mathematical analysis of a well-known numerical approach used in molecular
dynamics to efficiently sample a coarse-grained description of the original trajectory (in …

We establish a fundamental isomorphism between discrete-time balanced urn processes
and certain ordinary differential systems, which are nonlinear, autonomous, and of a simple …

This paper reviews P´ olya urn models and their connection to random trees. Basic results
are presented, together with proofs that underly the historical evolution of the accompanying …

Random binary search trees, b-ary search trees, median-of-(2k+ 1) trees, quadtrees, simplex
trees, tries, and digital search trees are special cases of random split trees. For these trees …

We give a partial overview of some results from the rich theory of branching processes and
illustrate their use in the probabilistic analysis of algorithms and data structures. The …