"RANDOM MATRICES AND RELATED TOPICS" |
Monthly Colloquia |
Abstract: We generalize certain known matrix integrals (Harish-Chandra-Itzukson-Zuber, Gross-Witten, etc.) using a notion of tau-function of matrix argument. We also consider asymptotic expansion of some matrix integrals in terms of tau-functions of a hypergeometric type.
Abstract: Legitimacy of replica field theories has been a point of controvercy for over two decades. Inspired by an ongoing discussion, we critically review a so-called "replica symmetry breaking" approach, and claim exact integrability of nonlinear replica sigma models derived in the context of random matrix theories. This progress became possible due to a discovered connection between replica field theories and the theory of integrable hierarchies. Further applications of the formalism are briefly discussed.