Masha Shcherbina, Brunello Tirozzi
Rigorous Solution to the Gardner Problem
(609K, Postscript)
ABSTRACT. We prove rigorrously the well known result of Gardner about the
typical fractional volume of interactions between N spins which solve the
problem of storing a given set of p random patterns. The Gardner formula
for this volume in the limit N,p \to \infty, p/N \to \alpha
is proven for all values of \alpha. Besides, we prove a useful criterion
of the factorisation of all the correlation functions for a class
of spin glass models.