Replica Approach in Random Matrix Theory
Disordered Systems and Neural Networks
2009-11-19 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
This Chapter outlines the replica approach in Random Matrix Theory. Both fermionic and bosonic versions of the replica limit are introduced and its trickery is discussed. A brief overview of early heuristic treatments of zero-dimensional replica field theories is given to advocate an exact approach to replicas. The latter is presented in two elaborations: by viewing the replica partition function as the Toda Lattice and by embedding the replica partition function into a more general theory of functions.
Keywords
Cite
@article{arxiv.0909.3198,
title = {Replica Approach in Random Matrix Theory},
author = {Eugene Kanzieper},
journal= {arXiv preprint arXiv:0909.3198},
year = {2009}
}
Comments
Chapter for "The Oxford Handbook of Random Matrix Theory"; 23 pages; amended version (v2): typos corrected, a comment in Sec. 3.3.2 added; bibliography extended