Simone Franchini

most citedUniversal scaling limits for spin networks via martingale methods

1 citations · 1 across the 2 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 $H_{n} (h, I ¨ ) = \sum_{i = 1}^{n} h_{i} (I ¨ _{i} - m),$ where $(h_{i})$ are i.i.d.\ real random variables and $(I ¨ _{i})$ are i.i.d.\ Ising spins. We consider the energy levels…

cond-mat.stat-mech2026★ 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…

math.PR2026

REM universality for linear random energy

Francesco Concetti, Simone Franchini

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

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…