Persistence probability of random weyl polynomial

van Hao Can (1) , Viet-Hung Pham (2)

1 I2M - Institut de Mathématiques de Marseille
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we obtain the persistence exponents of random Weyl polynomials in both cases: the nonnegative axis and the whole real axis. Our result confirms the predictions given by Schehr and Majumdar \cite{SM2}. In the nonnegative axis case, Dembo and Mukherjee \cite{DM} gave an upper bound for the persistence exponent by considering the persistence probability on a suitable interval. Our main contribution is to prove this upper bound is the exact exponent and to extend to the whole real axis case.

Domaines: Probabilités [math.PR]

van Hao Can, Viet-Hung Pham. Persistence probability of random weyl polynomial. 2019. ⟨hal-01608950v2⟩