Simone Franchini

most citedUniversal scaling limits for spin networks via martingale methods

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

math.PR2026

REM universality and Poisson-Dirichlet Gibbs weights for linear random energy

Francesco Concetti, Simone Franchini

We study the Hamiltonian $H_{n} (h, σ) = \sum_{i = 1}^{n} h_{i} (σ_{i} - m),$ where $(h_{i})$ are i.i.d.\ real random variables and $(σ_{i})$ are i.i.d.\ Ising spins. We consider the energy levels obt…

math.PR2026

REM universality for linear random energy

Francesco Concetti, Simone Franchini

We consider a sequence of random Hamiltonians $H_{n} (h, σ) = \sum_{i = 1}^{n} h_{i} (σ_{i} - m)$ , and study the asymptotic ( $n \to \infty$ ) distribution of the energy levels $(H_n(h,σ))_{σ\in \{-1,1…

cond-mat.stat-mech2026

Constructive Cavity Method

Simone Franchini

We show that the functional appearing in the celebrated Parisi formula for the free energy of the Sherrington-Kirkpatrick model can be found from the incremental free energy obtain…

cond-mat.stat-mech2024★ 1 cited

Universal scaling limits for spin networks via martingale methods

Simone Franchini

We use simple martingale methods to construct a large deviation theory of spin systems with pairwise interactions. As an application, we show that the fully connected case obeys a…