Gaussians, Groups, and Renormalization.

Abstract: Abstract: Gaussian (a.k.a. normal) probability distributions are ubiquitous. One reason for this is the fact that the set of Gaussian distributions is closed under multiple operations---subspace restriction, fiberwise integration, disjoint multiplication, pointwise multiplication, convolution. Also, as Heisenberg and Dirac realized in the early days of quantum mechanics, the Gaussian distribution may be characterized uniquely as the fixed point of a group action. In this talk, we will show how the aforementioned operations on distributions correspond to operations on groups. This provides a systematic, functorial, and generalizable approach to deriving and understanding properties of Gaussian distributions.

My interest in this topic comes from a joint project with Sam McCrosson on renormalization in quantum field theory. We used this group-theoretic approach to Gaussian distributions to derive the renormalization flow from the path integral. After a quick but self-contained introduction to renormalization, I will give an overview of this project as a practical application of the ideas presented here.

Computer scienceMathematics

Audience: researchers in the topic

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New York City Category Theory Seminar

Series comments: The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York

Some talks will be in-person (with a Zoom connection) and some talks will only be on Zoom. Time: Wednesdays 02:00-3:00 PM Eastern Time (US and Canada) NOTICE NEW TIME!!!

IN-PERSON INFORMATION: 365 Fifth Avenue (at 34th Street) map (Diagonally across from the Empire State Building) New York, NY 10016-4309 Room 4214.03 NOTICE NEW ROOM!!! THere will be a Zoom link to join us on in-person talks. This means that from now on, in-person talks will be hybrid.

ZOOM INFORMATION: brooklyn-cuny-edu.zoom.us/j/84134080992?pwd=MNvAvOfYemk2bh7qCtI9I5zQTRkFdR.1 Meeting ID: 841 3408 0992 Passcode: NYCCTS

Seminar web page. Videoed talks. Previous semesters. List of previous speakers. Researchseminars.org page.

Co-organizers: Emilio Minichiello and Noson S. Yanofsky.

Contact E. Minichiello or N. Yanofsky to schedule a speaker or to add a name to the seminar mailing list.

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