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 …

Consider a collection of N Brownian bridges B_i:-N,N→R, B i (− N)= B i (N)= 0, 1≤ i≤ N,
conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a …

While the widespread emergence of nanoscience and nanotechnology can be dated back to
the early eighties, the last decade has witnessed a true coming of age of this research field …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

" The material covered in this book involves important and nontrivial results in contemporary
probability theory motivated by polymer models, as well as other topics of importance in …

This article provides an overview of the critical behaviour of the self-avoiding walk model on
Zd, and in particular discusses how this behaviour differs as the dimension d is varied. The …

This is a primer on a mathematically rigorous renormalisation group theory, presenting
mathematical techniques fundamental to renormalisation group analysis such as Gaussian …

Probabilistic models of directed polymers in random environment have received
considerable attention in recent years. Much of this attention has focused on integrable …

These lecture notes provide a rapid introduction to a number of rigorous results on self-
avoiding walks, with emphasis on the critical behaviour. Following an introductory overview …

We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …