Talks tomorrow: Najnudel and Aggarwal

[Balint Virag]

Dear All,

Tomorrow we will have two talks in the Toronto Probability Seminar. Both
in Fields 210. We will also have lunch with the speakers at 12:10pm we
will meet in Bahen at the south elevators on the first floor (next to
the former Cube). Let us know if you are interested in joining.

2:10 pm

Joseph Najnudel,
Bristol

The bead process for beta ensembles

Abstract: The bead process introduced by Boutillier is a countable
interlacing of the determinantal sine-kernel point processes. We
construct the bead process for general sine beta processes as an
infinite dimensional Markov chain whose transition mechanism is
explicitly described. We show that this process is the microscopic
scaling limit in the bulk of the Hermite beta corner process introduced
by Gorin and Shkolnikov, generalizing the process of the minors of the
Gaussian unitary and orthogonal ensembles.

3:10 pm

Amol Aggarwal
Columbia

A characterization for the Airy line ensemble

The Airy line ensemble is a universal scaling limit that is believed
(and in some cases proven) to govern the fluctuations of many
probabilistic systems, such as random surfaces, interacting particle
systems, and stochastic interfaces. It is an example of a "Brownian line
ensemble," which informally means that it is an infinite, ordered
sequence of random continuous curves that look like non-intersecting
Brownian motions. In this talk we survey recent results characterizing
the Airy line ensemble as the unique Brownian line ensemble whose top
curve decays parabolically, and we explain why this result is useful for
proving convergence theorems for various discrete stochastic models.
This is based on joint work with Jiaoyang Huang.