Rigorous Solution of the Gardner Problem
Abstract
We prove rigorously 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 random patterns. The Gardner formula for this volume in the limit N,p ∞, p/N α is proven for all values of α. Besides, we prove a useful criterion of the factorisation of all the correlation functions for a class of spin glass model.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.