Seminar on Stochastic Processes

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14 April 2021
17:15-19:00

Laurent Saloff-Coste
Cornell University

Event Details

Title	On random walks on "pocket groups"
Speaker, Affiliation	Laurent Saloff-Coste, Cornell University
Date, Time	14 April 2021, 17:15-19:00
Location	Zoom

On random walks on "pocket groups"

Zoom

28 April 2021
17:15-19:00

Prof. Dr. Yuansi Chen
Duke University

Event Details

Title	Recent progress on the KLS conjecture and Eldan’s stochastic localization scheme
Speaker, Affiliation	Prof. Dr. Yuansi Chen, Duke University
Date, Time	28 April 2021, 17:15-19:00
Location	Zoom
Abstract	Kannan, Lovász and Simonovits (KLS) conjectured in 1995 that the Cheeger isoperimetric coefficient of any log-concave density is achieved by half-spaces up to a universal constant factor. This conjecture also implies other important conjectures such as Bourgain's slicing conjecture (1986) and the thin-shell conjecture (2003). In this talk, first we briefly survey the origin and the main consequences of these conjectures. Then we present the development and the refinement of the main proof technique, Eldan's stochastic localization scheme. Finally we explain a few proof details which result in the current best bound of the Cheeger isoperimetric coefficient in the KLS conjecture.

Recent progress on the KLS conjecture and Eldan’s stochastic localization schemeread_more

Zoom

12 May 2021
17:15-19:00

Prof. Dr. Konstantin Tikhomirov
Georgia Institute of Technology

Event Details

Title	Singularity of random Bernoulli matrices
Speaker, Affiliation	Prof. Dr. Konstantin Tikhomirov, Georgia Institute of Technology
Date, Time	12 May 2021, 17:15-19:00
Location	Zoom
Abstract	For each n, let Bn be an n-by-n matrix with i.i.d. entries taking values +1 and -1. We show that the probability that Bn is singular, is of order (1/2+o(1))ⁿ, where the quantity o(1) converges to zero as n grows to infinity. We shall further discuss a variation of the problem for sparse Bernoulli matrices, and give an overview of the recent progress in this line of research.

Singularity of random Bernoulli matricesread_more

Zoom

2 June 2021
17:15-19:00

Prof. Dr. Daniel Remenik
Department of Mathematical Engineering, Universidad de Chile

Event Details

Title	Some recent progress on the KPZ fixed point
Speaker, Affiliation	Prof. Dr. Daniel Remenik, Department of Mathematical Engineering, Universidad de Chile
Date, Time	2 June 2021, 17:15-19:00
Location	Zoom
Abstract	The KPZ fixed point is the Markov process which arises as the universal scaling limit of all models in the KPZ universality class, a broad collection of models including one-dimensional random growth, directed polymers and particle systems. It contains all of the rich fluctuation behavior seen in the class, which for some initial data relates to distributions from random matrix theory. In this talk I'm going to introduce this process and discuss some of the recent progress in its study by several groups of authors, including questions about the construction of the process, about its universality and integrability, and about detailed descriptions of some of its properties.

Some recent progress on the KPZ fixed pointread_more

Zoom

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