4 papers
Partial sums of random multiplicative functions with supercritical divisor twists
Jad Hamdan
Let be a Steinhaus random multiplicative function, and for , let denote the -divisor function. For we establish that $$ \mathbb{E}\bigg\{…
On the Fourier coefficients of critical Gaussian multiplicative chaos
Louis-Pierre Arguin, Jad Hamdan
We continue the study of the Fourier coefficients of Gaussian multiplicative chaos (GMC) recently initiated by Garban and Vargas. We show that if are the Fourie…
Genus expansion for non-linear random matrix ensembles with applications to neural networks
Nicola Muca Cirone, Jad Hamdan, Cristopher Salvi
We present a unified approach to studying certain non-linear random matrix ensembles and associated random neural networks at initialization. This begins with a novel series expans…
The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals
Louis-Pierre Arguin, Jad Hamdan
We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed , large , and $y…