2009/09/17 by Eugene Kanzieper, Kanzieper, Eugene
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.0909.3198
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
openalex publication_date 2009/09/17 · arxiv created 2009/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 β=2 replica partition function as the Toda Lattice and by embedding the replica partition function into a more general theory of τ functions.