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Fractal Geometry of the KPZ equation

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

October 21, 2021 (01:30 PM PDT - 02:20 PM PDT)
Speaker(s): Promit Ghosal (Massachusetts Institute of Technology)
Location: MSRI: Simons Auditorium, Online/Virtual
  • KPZ equation

  • Cole-Hopf solution

  • fractal properties

  • Gibbsian line ensemble

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The Kardar-Parisi-Zhang (KPZ) equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle systems, random polymers etc. In this talk, we focus on how the tall peaks and deep valleys of the KPZ height function grow as time increases. In particular, we will ask what are the appropriate scaling of the peaks and valleys of the KPZ equation and whether they converge to any limit under those scaling. These questions will be answered via the law of iterated logarithms and fractal dimensions of the level sets.

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