## 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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## Acknowledgements

We would like to thank anonymous referees for carefully reading the manuscript and many valuable comments. The first author is supported by the fellowship of the Japan Society for the Promotion of Science and the Grant-in-Aid for JSPS fellows Number 17F17319. The second author is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2017.316.

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Can, V.H., Pham, VH. Persistence Probability of Random Weyl Polynomial.
*J Stat Phys* **176**, 262–277 (2019). https://doi.org/10.1007/s10955-019-02298-0

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DOI: https://doi.org/10.1007/s10955-019-02298-0