4 papers
Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators
Brian C. Hall, Ching-Wei Ho, Jonas Jalowy +1
We start with a random polynomial of degree with independent coefficients. We then consider a new polynomial obtained by applications o…
The heat flow, GAF, and SL(2;R)
Brian Hall, Ching-Wei Ho, Jonas Jalowy +1
We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian a…
Repeated differentiation and free unitary Poisson process
Zakhar Kabluchko
We investigate the hydrodynamic behavior of zeroes of trigonometric polynomials under repeated differentiation. We show that if the zeroes of a real-rooted, degree trigonometri…
Lee--Yang zeroes of the Curie--Weiss ferromagnet, unitary Hermite polynomials, and the backward heat flow
Zakhar Kabluchko
The backward heat flow on the real line started from the initial condition results in the classical -th Hermite polynomial whose zeroes are distributed according to the Wi…