A note on the polynomial moments of the partition function in the SK model

Abstract

We prove a simple identity relating the $k$th moment of the partition function $Z_N(\cdot )$ in the SK model to the $N$th moment of the partition function $Z_k(\cdot )$. As a corollary we find a characterisation of the limit ${\lim }_{N\to \infty }\frac{1}{N}\log \mathbb{E}{Z}_N(\beta {)}^k$ alternative to the one found previously by Michel Talagrand in \cite{4}.

arXiv comment17 pages