Upper bound of some character ratios and large genus asymptotic behavior of Hurwitz numbers
Abstract
In [14] we found the large genus asymptotics of Hurwitz numbers for the Riemann sphere with a fixed number of general profiles and some (2,1d-2) profiles. In this paper, motivated from [3], we generalize these results to Hurwitz numbers of an arbitrary compact Riemann surface with a fixed number of general profiles and some (r,1d-r) profiles.
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