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Abstract: In a generalized Airy matrix model, a power $p$ replaces the cubic term ofthe Airy model introduced by Kontsevich. The parameter $p$ corresponds toWitten-s spin index in the theory of intersection numbers of moduli space ofcurves. A continuation in $p$ down to $p= -2$ yields a well studied unitarymatrix model, which exhibits two different phases in the weak and strongcoupling regions, with a third order critical point in-between. The applicationof duality and replica to the $p$-th Airy model allows one to recover both theweak and strong phases of the unitary model, and to establish some new resultsfor these expansions. Therefore the unitary model is also indirectly agenerating function for intersection numbers.



Autor: E.Brezin, S.Hikami

Fuente: https://arxiv.org/



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