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Gibbsian Line Ensembles and Beta-Corners Processes

[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021

October 18, 2021 (01:30 PM PDT - 02:20 PM PDT)
Speaker(s): Evgeni Dimitrov (Columbia University)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • Gibbsian line ensembles

  • avoiding random walks

  • KPZ universality

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Abstract

Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability.

Gibbsian line ensembles can be thought of as collections of finite or countably infinite independent random walkers whose distribution is reweighed by the sum of local interactions between the walkers. I will discuss some recent progress in the asymptotic study of Gibbsian line ensembles, summarizing some joint works with Barraquand, Corwin, Matetski, Wu and others.

Beta-corners processes are Gibbs measures on triangular arrays of interacting particles and can be thought of as analogues/extensions of multi-level spectral measures of random matrices. I will discuss some recent progress on establishing the global asymptotic behavior of beta-corners processes, summarizing some joint works with Das and Knizel.

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91769?type=thumb Gibbsian Line Ensembles and Beta-Corners Processes 2.64 MB application/pdf Download
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