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APRG Seminar

Title: Hirschman–Widder densities and their preservers
Speaker: Alexander Belton (Lancaster University, Lancaster, UK)
Date: 20 April 2022
Time: 4 pm
Venue: Microsoft Teams (online)

Hirschman–Widder densities may be viewed as the probability density functions of positive linear combinations of independent and identically distributed exponential random variables. They also arise naturally in the study of Pólya frequency functions, that is, integrable functions which give rise to totally positive Toeplitz kernels. This talk will introduce this class of densities and discuss some of its properties. We will demonstrate connections to Schur polynomials and to orbital integrals. We will conclude by describing the rigidity of this class under composition with polynomial functions.

This is joint work with Dominique Guillot (University of Delaware), Apoorva Khare (Indian Institute of Science, Bangalore) and Mihai Putinar (University of California at Santa Barbara and Newcastle University).

The video of this talk is available on the IISc Math Department channel.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 May 2024