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math.PR2024
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…
math.NT2024
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…