Abstract
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 (J Stat Phys 132(2):235–273, 2008). In the nonnegative axis case, Dembo and Mukherjee (Ann Probab 43(1):85–118, 2015) 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.
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