Replica Approach in Random Matrix Theory

Details Replica Approach in Random Matrix Theory Replica Approach in Random Matrix Theory

2009-09-17

arxiv.org/abs/0909.3198v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

Chapter for "The Oxford Handbook of Random Matrix Theory"; 23 pages; amended version (v2): typos corrected, a comment in Sec.

Scientific paper

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 $\beta=2$ replica partition function as the Toda Lattice and by embedding the replica partition function into a more general theory of $\tau$ functions.

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