Thibault Pautrel

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20202026

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math.PR2026

Global universality of the expected number of zeros of non-analytic random signals

Jürgen Angst, Thibault Pautrel, Guillaume Poly

We study the asymptotics as $n$ goes to infinity of $E [N (S_{n}, [0, 2 π])]$ , the expected number of zeros in $[0, 2 π]$ of a random periodic signal $S_{n}$ of…

math.PR2021

Real zeros of random trigonometric polynomials with dependent coefficients

Jürgen Angst, Thibault Pautrel, Guillaume Poly

We further investigate the relations between the large degree asymptotics of the number of real zeros of random trigonometric polynomials with dependent coefficients and the underl…

math.PR2020

New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients

Thibault Pautrel

We consider random trigonometric polynomials of the form \[ f_n(t):=\frac{1}{\sqrt{n}} \sum_{k=1}^{n}a_k \cos(k t)+b_k \sin(k t), \] where $(a_{k})_{k \geq 1}$ and $(b_{k})_{k \geq 1}$ a…