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Loop equations and topological recursion for the arbitrary-$β$ two-matrix model
Loop equations topological recursion two-matrix model
2011/7/25
Abstract: We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading ord...
Average characteristic polynomials in the two-matrix model
Two-matrix model average characteristic polynomial
2010/12/6
The two-matrix model is defined on pairs of Hermitian matrices (M1,M2) of size n × n by the probability measure 1 Zn exp (Tr(−V (M1) −W(M2) + M1M2)) dM1 dM2, where V and W are given poten...