Seminar on stochastic processes

Members of the probability group are involved in co-organizing remote specialized seminars that take place on Tuesdays and Thursdays:

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Datum / Zeit

Referent:in

Titel

Ort

14. April 2021
17:15-19:00

Laurent Saloff-Coste
Cornell University

Details

Titel	On random walks on "pocket groups"
Referent:in, Affiliation	Laurent Saloff-Coste, Cornell University
Datum, Zeit	14. April 2021, 17:15-19:00
Ort	Zoom

On random walks on "pocket groups"

Zoom

28. April 2021
17:15-19:00

Prof. Dr. Yuansi Chen
Duke University

Details

Titel	Recent progress on the KLS conjecture and Eldan’s stochastic localization scheme
Referent:in, Affiliation	Prof. Dr. Yuansi Chen, Duke University
Datum, Zeit	28. April 2021, 17:15-19:00
Ort	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. Mai 2021
17:15-19:00

Prof. Dr. Konstantin Tikhomirov
Georgia Institute of Technology

Details

Titel	Singularity of random Bernoulli matrices
Referent:in, Affiliation	Prof. Dr. Konstantin Tikhomirov, Georgia Institute of Technology
Datum, Zeit	12. Mai 2021, 17:15-19:00
Ort	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. Juni 2021
17:15-19:00

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

Details

Titel	Some recent progress on the KPZ fixed point
Referent:in, Affiliation	Prof. Dr. Daniel Remenik, Department of Mathematical Engineering, Universidad de Chile
Datum, Zeit	2. Juni 2021, 17:15-19:00
Ort	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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