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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 (Brandeis University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Tags/Keywords
  • KPZ equation

  • Cole-Hopf solution

  • fractal properties

  • Gibbsian line ensemble

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Fractal Geometry Of The KPZ Equation

Abstract

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.

Supplements
91824?type=thumb Fractal Geometry of the KPZ equation 8.23 MB application/pdf Download
Video/Audio Files

Fractal Geometry Of The KPZ Equation

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