The conformal bootstrap was proposed in the 1970s as a strategy for calculating the
properties of second-order phase transitions. After spectacular success elucidating two …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996)
proposed a remarkable explicit expression, the so-called-M DOZZ formula, for the three …

arXiv:1207.4990v3 [math.FA] 1 Dec 2012 Page 1 arXiv:1207.4990v3 [math.FA] 1 Dec 2012
Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some …

We show how to combine our earlier results to deduce strong convergence of the interfaces
in the planar critical Ising model and its random-cluster representation to Schramm's SLE …

This article studies the planar Potts model and its random-cluster representation. We show
that the phase transition of the nearest-neighbor ferromagnetic q-state Potts model on Z^ 2 Z …

We consider the question of conformal invariance of the long-range Ising model at the
critical point. The continuum description is given in terms of a nonlocal field theory, and the …

Phase transitions are a central theme of statistical mechanics, and of probability more
generally. Lattice spin models represent a general paradigm for phase transitions in finite …

The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led
to spectacular predictions in the context of critical phenomena. It postulates an explicit …

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions
ensuring that a sequence of multi-linear polynomials of independent random variables …