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...

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Probability Seminar

How long does it take for a random walk to cover all the vertices of a graph?

And what is the structure of the uncovered set (the set of points not yet visited by the walk) close to the cover time?

We completely characterize the...

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...

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha