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math.PR2025
Overlap distribution of spherical spin glass models with general eigenvalue distribution of the interaction matrix
Debapratim Banerjee, Debabrata Jana
In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In pa…
math.PR2025
A short proof of free energy limit of two spin spherical Sherrington-Kirkpatrick model at any temperature
Debapratim Banerjee
In this paper, we present a short proof of the limit of free energy of spherical 2 spin Sherrington-Kirkpatrick (SSK) model without external field. This proof works for all tempera…
math.PR2025
Operator limit of Wigner matrices I
Debapratim Banerjee
We consider the Wigner matrix of dimension as . The objective of this paper is two folds: first we construct an operator on a suita…