The self-avoiding walk, and lattice spin systems such as the φ 4 model, are models of
interest both in mathematics and in physics. Many of their important mathematical problems …

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

We construct a family of quantum scalar fields over ap-adic spacetime which satisfy p-adic
analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the …

We consider the n n-component| φ|^ 4| φ| 4 spin model on Z^ 4 Z 4, for all n ≥ 1 n≥ 1, with
small coupling constant. We prove that the susceptibility has a logarithmic correction to …

We consider the critical behaviour of long-range O (n) O (n) models (n ≥ 0 n≥ 0) on Z^ d Z
d, with interaction that decays with distance r as r^-(d+ α) r-(d+ α), for α ∈ (0, 2) α∈(0, 2). For …

The study of matter fields on an ensemble of random geometries is a difficult problem still in
need of new methods and ideas. We will follow a point of view inspired by probability theory …

Abstract We consider long‐range Bernoulli bond percolation on the dd‐dimensional
hierarchical lattice in which each pair of points xx and yy are connected by an edge with …

Abstract We prove| x|^-2| x|-2 decay of the critical two-point function for the continuous-time
weakly self-avoiding walk on Z^ d Z d, in the upper critical dimension d= 4. This is a …

We prove up-to-constants bounds on the two-point function (ie, point-to-point connection
probabilities) for critical long-range percolation on the d-dimensional hierarchical lattice …

We consider the n-component| φ|^ 4| φ| 4 lattice spin model (n ≥ 1 n≥ 1) and the weakly
self-avoiding walk (n= 0 n= 0) on\mathbb Z^ d Z d, in dimensions d= 1, 2, 3 d= 1, 2, 3. We …