Title: Universality of Persistence of Random Polynomials
Abstract: We study the probability that a random polynomial has no real zeros. For a broad class of random polynomials with independent, mean-zero, finite-variance coefficients and regularly varying deterministic weights, we show that this probability decays polynomially with the degree of the polynomial. The decay rate is universal and is determined by the persistence exponent of an associated stationary Gaussian process. Our result extends earlier work by removing Gaussianity and strong moment assumptions. In the special case of identically distributed coefficients without deterministic scaling, this confirms a conjecture of Poonen and Stoll on random polynomials with independent coefficients. Joint work with Sumit Mukherjee.
Reza Gheissari
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