We discuss several connections between discrete and continuous random trees. In the
discrete setting, we focus on Galton-Watson trees under various conditionings. In particular …

In these lectures, we give an account of certain recent developments of the theory of spatial
branching processes. These developments lead to several fas cinating probabilistic objects …

In this paper, a surprising connection is described between a specific brand of random
lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion …

This book focuses on percolation on high-dimensional lattices. We give a general
introduction to percolation, stating the main results and defining the central objects. We …

We show that there exist universal constants C (r)<∞ such that, for all loopless graphs G of
maximum degree [les] r, the zeros (real or complex) of the chromatic polynomial PG (q) lie in …

The self-avoiding walk is a classical model in statistical mechanics, probability theory and
mathematical physics. It is also a simple model of polymer entropy which is useful in …

We consider independent Bernoulli bond percolation on the integer lattice Zd, with edge
(bond) set consisting of pairs {x, y} of vertices of Zd with y− x∈ Ω, where Ω defines either the …

We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and
bond lattice animals on ${\mathbb {Z}^ d} $, having long finite-range connections, above …

In the last decade there has been an enormous progress in the mathematical understanding
of one-dimensional polymer measures, which are path measures that suppress self …

The purpose of these lectures is to present basic matrix models as practical combinatorial
tools, that turn out to be “exactly solvable. In short, a matrix model is simply a statistical …