Persistence probability of random weyl polynomial

TL;DR

This paper calculates the persistence exponents of random Weyl polynomials on different axes, confirming previous theoretical predictions and advancing understanding of their long-term behavior.

Contribution

It applies a specific method to derive persistence exponents for random Weyl polynomials, extending prior work to new cases.

Findings

Persistence exponents for Weyl polynomials on half nonnegative axis

Persistence exponents for Weyl polynomials on the entire real axis

Confirmation of Schehr and Majumdar's predictions

Abstract

In this paper, using the method proposed by Dembo and Mukherjee [5], we obtain the persistence exponents of random Weyl polynomials in both cases: half nonnegative axis and the whole real axis. Our result is a confirmation to the predictions of Schehr and Majumdar [22].