Asymptotic behavior of the magnetization for the perceptron model

David Marquez-Carreras (1) , Carles Rovira (1) , Samy Tindel (2)

1 UB - Departament de Probabilitats
2 IECN - Institut Élie Cartan de Nancy

In this paper, we show that, in case of a perceptron model for which the number of outputs is a small proportion of the size of the system, the limiting behavior of the magnetization of a given spin, namely the random variable $\langle\si_k\rangle$, can be identified. In fact, we prove a $L^2$ convergence for a collection of those random variables.

Mots clés: spin glasses; perceptron model; cavity method

Domaines: Probabilités [math.PR]

David Marquez-Carreras, Carles Rovira, Samy Tindel. Asymptotic behavior of the magnetization for the perceptron model. 2005. ⟨hal-00151194⟩