Random Matrices and Dynamics of Optimization in Very High Dimensions (3/4)
By Gérard Ben Arous
Random Matrices and Dynamics of Optimization in Very High Dimensions (1/4)
By Gérard Ben Arous
Appears in collection : Zeta Functions / Fonctions Zêta
In this talk I will discuss questions concerning the asymptotic behavior of the Epstein zeta function $E_{n}\left ( L, s \right )$ in the limit of large dimension $n$. In particular I will be interested in the behavior of $E_{n}\left ( L, s \right )$ for a random lattice $L$ of large dimension $n$ and $s$ a complex number in the critical strip. Along the way we will encounter certain random functions that are closely related to $E_{n}\left ( L, s \right )$ and interesting in their own right.