Department of Mathematics Calendar

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Probability Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
347 Altgeld Hall
Date
Nov 29, 2022   2:00 - 2:50 pm  
Speaker
Christopher Janjigian, Purdue University
Contact
Partha Dey
Views
20
Title:    Ergodicity and synchronization of the KPZ equation.
 
Abstract:    The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to have stationary distributions modulo additive constants given by Brownian motion with drift. In this talk, we will discuss some recent results which show that these distributions are totally ergodic and present progress toward the conjecture that these are the only ergodic stationary distributions of the KPZ equation. We study these problems through the lens of the synchronization by noise phenomenon and establish what is known as a one force — one solution principle: the solution to the KPZ equation (modulo an additive constant) started in the distant past from an initial condition with a given slope will converge almost surely to a Brownian motion with that drift for all but a random (possibly empty) countable set of slopes. The family of Brownian motions obtained in this way is known as the Busemann process for the equation and forms our main tool for studying these questions. Joint work with Firas Rassoul-Agha (Utah) and Timo Seppäläinen (Madison)
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