Suppose we immerse a large porous stone in a bucket of water. What is the probability that
the centre of the stone is wetted? In formulating a simple stochastic model for such a …

This course aims to be a (nearly) self-contained account of part of the mathematical theory of
percolation and related topics. The first nine chapters summarise rigorous results in …

Spin glasses are disordered magnetic systems that have led to the development of
mathematical tools with an array of real-world applications, from airline scheduling to neural …

We review recent theoretical progress on glassy dynamics, with special emphasis on the
importance and universality of the aging regime, which is relevant to many experimental …

In this topical review we discuss the nature of the low-temperature phase in both infinite-
ranged and short-ranged spin glasses. We analyse the meaning of pure states in spin …

For a very general class of probability distributions in disordered Ising spin systems, in the
thermodynamical limit, we prove the following property for overlaps among real replicas …

Abstract Preface; 1. Introduction; Part I. Spin-Glass Systems: 2. Physics of the spin glass
state; 2. The mean-field theory of spin glasses; 4. Physics of replica symmetry breaking; 5 …

Monte Carlo simulations are methods for simulating statistical systems. The aim is to
generate a representative ensemble of configurations to access thermodynamical quantities …

We study via renormalization group (RG), numerics, exact bounds, and qualitative
arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random …

The nature of the zero-temperature ordering transition in the three-dimensional Gaussian
random-field Ising magnet is studied numerically, aided by scaling analyses. Various …