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Marked and Conditional Determinantal Point Processes

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

October 22, 2021 (10:20 AM PDT - 11:10 AM PDT)
Speaker(s): Tom Claeys (Université Catholique de Louvain)
Location: MSRI: Simons Auditorium, Online/Virtual
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Abstract

I will introduce a family of marked determinantal point processes and associated conditional ensembles, in which information about a random part of a point configuration is encoded. Special cases of these conditional ensembles appear in the Its-Izergin-Korepin-Slavnov method and in the study of number rigidity. I will discuss general properties of these ensembles, and show how they lead to a strengthened notion of number rigidity for determinantal point processes induced by a certain class of orthogonal projections, including the sine, Airy, and Bessel point processes. The talk will be based on joint work with Gabriel Glesner.

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