Influences for Convex Sets

Start Date: April 24, 2023
Event Start Time: 2:00 PM
Event End Time: 3:00 PM
Seminar Series: Rutgers Discrete Mathematics Seminar
Presenter(s): Shivam Nadimpalli - Columbia University
Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
Event Additional Info: <p>See: <a href="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
Presentation Type: Stand Alone Presentation
Abstract:
We introduce a new notion of influence—called "convex influence"—for convex sets over Gaussian space which has many of the properties of influences of Boolean functions over the hypercube. Our main results for convex influences give Gaussian space analogues of many important results on influences for monotone Boolean functions, including the Kahn-Kalai-Linial theorem, a sharp threshold theorem of Kalai, and a quantitative correlation inequality due to Talagrand. Time permitting, we will also discuss a recent application of convex influences to the problem of testing convex truncation, a natural algorithmic task in high-dimensional statistics.

Based on joint works with Anindya De and Rocco A. Servedio.

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