In this article, we consider the following family of random trigonometric polynomials p_n (t,
Y)= ∑ _ k= 1^ n Y_ k^ 1\cos (kt)+ Y_ k^ 2\sin (kt) pn (t, Y)=∑ k= 1 n Y k 1 cos (kt)+ Y k 2 sin …

We consider random trigonometric polynomials of the form\[f_n (x, y)=\sum _ {1\le k, l\le n} a_
{k, l}\cos (kx)\cos (ly),\] where the entries $(a_ {k, l}) _ {k, l\ge 1} $ are iid random variables …

We investigate the local distribution of roots of random functions of the form $ F_n (z)=\sum_
{i= 1}^ n\xi_i\phi_i (z) $, where $\xi_i $ are independent random variables and $\phi_i (z) …

In this paper, we study the number of real roots of random trigonometric polynomials with iid
coefficients. When the coefficients have zero mean, unit variance and some finite high …

On some probability space (Ω, F, P), we consider two independent sequences (ak) k≥ 1 and
(bk) k≥ 1 of iid random variables that are centered with unit variance and which admit a …

We consider random trigonometric polynomials of the form\[f_n (t):=\sum _ {1\le k\le n} a_
{k}\cos (kt)+ b_ {k}\sin (kt),\] whose coefficients $(a_ {k}) _ {k\ge 1} $ and $(b_ {k}) _ {k\ge 1} …

We prove a functional limit theorem in a space of analytic functions for the random Dirichlet
series D (α; z)=∑ n≥ 2 (log n) α (η n+ i θ n)/nz, properly scaled and normalized, where (η n …

Let ξ 0, ξ 1,… be iid random variables with zero mean and unit variance. Consider a random
Taylor series of the form f (z)=∑ k= 0∞ ξ kckzk, where c 0, c 1,… is a real sequence such …

We consider random orthonormal polynomials $$ P_ {n}(x)=\sum_ {i= 0}^{n}\xi_ {i} p_ {i}(x),
$$ where $\xi_ {0} $,..., $\xi_ {n} $ are independent random variables with zero mean, unit …

It has been shown in a recent work by Yakir-Zeitouni that the minimum modulus of random
trigonometric polynomials with Gaussian coefficients has a limiting exponential distribution …