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Abstract: Kontsevich-s work on Airy matrix integrals has led to explicit results forthe intersection numbers of the moduli space of curves. In this article we showthat a duality between k-point functions on $N\times N$ matrices and N-pointfunctions of $k\times k$ matrices, plus the replica method, familiar in thetheory of disordered systems, allows one to recover Kontsevich-s results on theintersection numbers, and to generalize them to other models. This provides analternative and simple way to compute intersection numbers with one markedpoint, and leads also to some new results.



Author: E. Brezin, S. Hikami

Source: https://arxiv.org/



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