This review provides an introduction to two dimensional growth processes. Although it
covers a variety of processes such as diffusion limited aggregation, it is mostly devoted to a …

We characterize and describe all random subsets $ K $ of a given simply connected planar
domain (the upper half-plane ${\mathbb H} $, say) which satisfy the “conformal restriction” …

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we
use to obtain large samples of walks on the cubic lattice of up to 33× 10 6 steps …

Abstract 1 Introduction 1.1 General Motivation 1.2 Loop-Erased Random Walks 1.3 Iterations
of Conformal Maps and SLE 1.4 The Critical Percolation Exploration Process 1.5 Chordal …

A coarse-grained simulation model eliminates microscopic degrees of freedom and
represents a polymer by a simplified structure. A priori, two classes of coarse-grained …

We study quantum JT gravity at finite cutoff using a mapping to the statistical mechanics of a
self-avoiding loop in hyperbolic space, with positive pressure and fixed length. The …

The thermal properties of coarse-grained knotted copolymer rings fluctuating in a highly
screening solution are investigated on a simple cubic lattice using the Wang-Landau Monte …

The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic
radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By …

We propose a measure of shape which is appropriate for the study of a complicated
geometric structure, defined using the topology of neighborhoods of the structure. One …

We implement a scale-free version of the pivot algorithm and use it to sample pairs of three-
dimensional self-avoiding walks, for the purpose of efficiently calculating an observable that …