Title: Probability and root dynamics of analytic functions
Abstract: We will discuss how a number of seemingly simple conjectures on the roots of analytic functions can be translated to limit theorems in probability. In particular, we will see that if f is an even entire function from what is known as the Laguerre--Pólya class, then the roots of f^{(2n)} form a lattice as n tends to infinity, and how this result follows from a central limit theorem for certain empirical measures. Time permitting, we will discuss a more general connection between differential operators g(tD), where g is some appropriate entire function, and (free) Lévy processes at time t. Based on joint work with Jonas Jalowy, Sean O'Rourke, and David Renfre
Marcus Michelen
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