Department of Mathematics

Department of Mathematics Seminars and Talks

 

Seminar

Toronto Probability

Talk Information
Title
Random Averages on the Integer Lattice
Start date and time
15:10 on Monday April 14, 2025
Duration in minutes
50 (until 16:00 on Monday April 14, 2025)
Room
FI210, Fields Institute, 222 College St.
Streaming link
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Abstract

In the averaging process on a graph $G = (V, E)$, a random mass distribution $\eta$ on $V$ is repeatedly updated via transformations of the form $\eta_{v}, \eta_{w} \mapsto (\eta_{v} + \eta_{w})/2$, with updates made according to independent Poisson clocks associated to the edge set $E$. We'll discuss this process when the underlying graph $G$ is the integer lattice $\mathbb{Z}^{d}$. We show that it exhibits tight asymptotic concentration around its mean and use this to obtain a central limit theorem. The proof relies on reducing the original problem to one about an associated random walk on $\mathbb{Z}^{d}$, a technique which is likely adaptable to similar processes.

Note

Speaker Institution: Toronto Metropolitan University

Speaker Information
Full Name
Austin Eide
Personal website
Institution
Toronto Metropolitan University
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