Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
SciPost Phys. 12, 125 (2022) ·
published 11 April 2022
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The Wigner spiked model in a mismatched setting is studied with the finite
temperature Statistical Mechanics approach through its representation as a
Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution
of the model with Ising spins is rigorously proved to be given by a variational
principle on two order parameters, the Parisi overlap distribution and the
Mattis magnetization. The latter is identified by an ordinary variational
principle and turns out to concentrate in the thermodynamic limit. The solution
leads to the computation of the Mean Square Error of the mismatched
reconstruction. The Gaussian signal distribution case is investigated and the
corresponding phase diagram is identified.
Dr Camilli: "Comments on the Weaknesses sec..."
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