Can you hear the shape of LQG? We obtain a Weyl law for the
eigenvalues of Liouville Brownian motion: the n-th eigenvalue grows
linearly with n, with the proportionality constant given by the
Liouville area of the domain (times a certain...
I will start by introducing and motivating the (two-component)
Coulomb gas on the d-dimensional lattice Zd. I will then present
some puzzling properties of the fluctuations of this Coulomb gas.
The connection of this model with integer-valued fields...
We will discuss stochastic quantization i.e. Langevin dynamic of
the Yang-Mills model on two and three dimensional torus. This is
described by a Lie algebra valued stochastic PDE driven by
space-time white noise. We construct (local) solution to...
We consider a Poisson point process on Rd with intensity lambda
for d greater than or = 2. On each point, we independently center a
ball whose radius is distributed according to some power-law
distribution mu. When the distribution mu has a finite d...
For each central charge c∈(0,1], we construct a conformally
invariant field which is a measurable function of the local time
field L of the Brownian loop soup with intensity c and i.i.d. signs
given to each cluster. This field is canonically...
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...
