10th World Congress in Probability and Statistics

Plenary Lectures

Plenary Tue-1

IMS Medallion Lecture (Laurent Saloff-Coste)

9:00 AM — 10:00 AM KST
Jul 19 Mon, 8:00 PM — 9:00 PM EDT

Gambler's ruin problems

Laurent Saloff-Coste (Cornell University)

The classical gambler’s ruin problem asks for the probability that player A wins all the money in a fair game between two players, A and B.
For this lecture, our starting point is a fair game of this sort involving three players, A, B, and C, holding a total on N tokens. That's already quite interesting. More generally, I will discuss techniques that allow us to understand the behavior of certain finite Markov chains before the time the chain is absorbed at a given boundary. This is based on joint work with Persi Diaconis and Kelsey Houston-Edwards.

Session Chair

Qi-Man Shao (Chinese University of Hong Kong)

Plenary Tue-2

IMS Medallion Lecture (Elchanan Mossel)

10:00 AM — 11:00 AM KST
Jul 19 Mon, 9:00 PM — 10:00 PM EDT

Simplicity and complexity of belief-propagation

Elchanan Mossel (Massachusetts Institute of Technology)

Belief Propagation is a very simple and popular algorithm for the inference of posteriors for probability models on trees based on iteratively applying Bayes' rule. It is widely used in coding theory, in machine learning, in evolutionary inference, among other areas. We will survey the distributional properties and statistical efficiency of Belief Propagation in some of the simplest models and applications of these to phylogenetic reconstruction and to detection of block models. Finally, we will discuss the computational complexity of this seemingly simple algorithm.

Session Chair

Krzysztof Burdzy (University of Washington)

Plenary Tue-3

Levy Lecture (Massimiliano Gubinelli)

7:00 PM — 8:00 PM KST
Jul 20 Tue, 6:00 AM — 7:00 AM EDT

A variational method for Euclidean quantum fields

Massimiliano Gubinelli (University of Bonn)

I will talk about recent progresses in understanding the probabilistic structure of certain (bosonic) Euclidean Quantum Field theories in terms of a variational representation of their Laplace transform. This approach gives an alternative construction of the $\Phi^4_3$ measure in finite volume and a tool to investigate some of its properties. It also generates some new interesting mathematical objects like a new kind of equations which allows to describe the infinite volume measures.

Session Chair

Martin Hairer (Imperial College London)

Plenary Tue-4

Doob Lecture (Nicolas Curien)

8:00 PM — 9:00 PM KST
Jul 20 Tue, 7:00 AM — 8:00 AM EDT

Parking on Cayley trees and Frozen Erdös-Rényi

Nicolas Curien (Paris-Saclay University)

Consider a uniform Cayley tree Tn with n vertices and let m cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives towards the root of the tree and park as soon as possible. Using combinatorial enumeration, Lackner & Panholzer established a phase transition for this process when m is approximately n/2. We couple this model with a variation of the classical Erdös-Rényi random graph process. This enables us to completely describe the phase transition for the size of the components of parked cars using a modification of the standard multiplicative coalescent which we named the frozen multiplicative coalescent. The geometry of critical parked clusters in the parking process is also studied. Those trees are very different from usual random trees and should converge towards the growth-fragmentation trees canonically associated to 3/2-stable process that already appeared in the study of random planar maps.

Based on joint work with Alice Contat

Session Chair

Wendelin Werner (Swiss Federal Institute of Technology Zürich)

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