An extensive update to a classic text Stochastic geometry and spatial statistics play a
fundamental role in many modern branches of physics, materials sciences, engineering …

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 …

Many phenomena in physics, chemistry, and biology can be modelled by spatial random
processes. One such process is continuum percolation, which is used when the …

Percolation theory was initiated some fifty years ago as a mathematical framework for the
study of random physical processes such as flow through a disordered porous medium. It …

Consider a Poisson process X in Rd with density 1. We connect each point of X to its k
nearest neighbors by undirected edges. The number k is the parameter in this model. We …

Continuum percolation models in which each point of a two-dimensional Poisson point
process is the centre of a disc of given (or random) radius $ r $, have been extensively …

We investigate random graphs on the points of a Poisson process in d-dimensional space,
which combine scale-free degree distributions and long-range effects. Every Poisson point …

We study the phase transition of random radii Poisson Boolean percolation: Around each
point of a planar Poisson point process, we draw a disc of random radius, independently for …

We study a general class of percolation models in Euclidean space including long-range
percolation, scale-free percolation, the weight-dependent random connection model and …