Probability Seminar

Conformal blocks are objects of fundamental importance in the bootstrap approach for exact solvability of 2D conformal field theory (CFT).  In this talk, we will present novel probabilistic expressions for them using the Gaussian free field in lieu...

We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the q^vol measure, corresponding to random cylindric partitions, the height...

It all began with card shuffling. Diaconis and Shahshahani studied the random transpositions shuffle; pick two cards uniformly at random and swap them. They introduced a Fourier analysis technique to prove that it takes 1/2nlogn steps to shuffle a...

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha 1, it had been predicted that these matrices exhibit an Anderson transition, also called a mobility edge, a point in the...

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on $\{1,\dots,2n\}$, one drawn above the real line and the other below the real line. Equivalently, a meandric system is a coupled...

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of SL_3-representations. Webs and...

The XY and the Villain models are models which exhibit the celebrated Kosterlitz-Thouless phase transitions in two dimensions. The spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, predicts that at low temperature, spin...

We consider a general system of interacting random loops which includes several models of interest, such as the spin O(N) model, the double dimer model, random lattice permutations, and is related to the loop O(N) model and to the interacting Bose...

The interchange process \sigma_T is a random permutation valued process on a graph evolving in time by transpositions on its edges at rate 1. On Z^d, when T is small all the cycles of the permutation \sigma_T are finite almost surely. In dimension d...

First-passage percolation studies the geometry obtained from a random perturbation of Euclidean geometry. In the discrete planar setting, one assigns random, independent and identically distributed, lengths to the edges of the lattice Z^2 and...