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math.PR2026
REM universality for linear random energy
Francesco Concetti, Simone Franchini
We consider a sequence of random Hamiltonians , and study the asymptotic () distribution of the energy levels $(H_n(h,σ))_{σ\in \{-1,1…
math.PR2025
Variational formula for the logarithmic potential of free additive convolutions
Francesco Concetti, David Belius, Giuseppe Genovese
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on . The formula is giv…
math.PR2024
On the determinant in Bray-Moore's TAP complexity formula
David Belius, Francesco Concetti, Giuseppe Genovese
In the computation of the TAP complexity, originally carried out by Bray and Moore, a fundamental step is to calculate the determinant of a random Hessian. As the replica method do…