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arXiv · 0909.3198

Replica Approach in Random Matrix Theory

Eugene Kanzieper
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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 $β=2$ replica partition function as the Toda Lattice and by embedding the replica partition function into a more general theory of $τ$ functions.

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Eugene Kanzieper. 2009-11-19. Replica Approach in Random Matrix Theory. https://arxiv.org/abs/0909.3198

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