Roots of random functions

Abstract: Random functions are linear combinations of deterministic functions using independent random coefficients. Several important examples are the Kac polynomial, Weyl polynomial, and random orthogonal polynomials. Random functions appear naturally in physics and approximation theory and remain mysterious despite decades of intensive research. We will present our approaches via the local universality method to study questions about the roots. As one of the applications, we prove that the number of real roots of a wide class of random polynomials satisfies the Central Limit Theorem.

Computer scienceMathematicsPhysics

Audience: researchers in the topic

Data Science and Computational Statistics Seminar