The Kontsevich Matrix Integral: Convergence to the Painlevé Hierarchy and Stokes’ Phenomenon
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DOI: 10.1007/s00220-017-2856-3
Abstract: We show that the Kontsevich integral on $${n\times n}$$n×n matrices ($${n < \infty}$$n read more here.
Keywords: painlev hierarchy; stokes phenomenon; kontsevich matrix; tau function ... See more keywords
Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes
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DOI: 10.1093/imrn/rnz168
Abstract: We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models.… read more here.
Keywords: gap; painlev hierarchy; point processes; solutions painlev ... See more keywords