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
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).