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Random Melting Skew Young diagram

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

October 19, 2021 (01:30 PM PDT - 02:20 PM PDT)
Speaker(s): Zhipeng Liu (University of Kansas)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • random melting skew Young diagram

  • argmax of the sum of two Airy processes

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Abstract

We consider a model of random melting skew Young diagram whose northwest and southeast corners melt independently at two rates $\gamma_1$ and $\gamma_2$ respectively. We find an exact formula for the joint distribution of the location of the last melting box and the melting time for an arbitrary initial skew Young diagram. This formula is suitable for asymptotic analysis for some special initial skew Young diagrams. As applications, we show how this result is related to the argmax of the sum of two independent Airy-type processes, such as two parabolic Airy2 processes, or a parabolic Airy2 process and an Airy1 process.

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