Title: Random Polynomials: Universality with Dependency

Abstract: In this talk, we explore random trigonometric polynomials with dependent coefficients, moving beyond the typical assumption of independent or Gaussian-distributed coefficients. We show that, under mild conditions on the dependencies between the coefficients, the asymptotic behavior of the expected number of real zeros is still universal. This universality result, to our knowledge, is the first of its kind for non-Gaussian dependent settings. Additionally, we present an elegant proof, highlighting the robustness of real zeros even in the presence of dependencies. Our findings bring the study of random polynomials closer to models encountered in practice, where dependencies between coefficients are common. Joint work with Jurgen Angst and Guillaume Poly.

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