Recent advances in single molecule experiments have raised many challenges. These
challenges can be met by a proper understanding of the inter-and intra-molecular …

Self-avoiding walks, lattice trees, and related geometrical models provide a link between the
physics of polymers and the study of critical phenomena. In particular, these models in the …

There is a simple way to" glue together" a coupled pair of continuum random trees (CRTs) to
produce a topological sphere. The sphere comes equipped with a measure and a space …

This book provides an introduction to lattice models of polymers. This is an important topic
both in the theory of critical phenomena and the modelling of polymers. The first two …

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms
of SLE (4). Specifically, there is a constant λ> 0 such that when h is an interpolation of the …

The statistical mechanics is considered of any polymer network with a prescribed topology,
in dimension d, which was introduced previously. The basic direct renormalization theory of …

The O (n) model on a two-dimensional dynamical random lattice is reformulated as a
random matrix problem. The critical properties of the model are encoded in the spectral …

Finite-size scaling and transfer-matrix techniques are used to determine the conformal
anomaly and critical exponents of O (n) models on the square lattice. These calculations …

A bstract Logarithmic conformal field theories have a vast range of applications, from critical
percolation to systems with quenched disorder. In this paper we thoroughly examine the …

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 …