104 citations · 576 across the 29 of their papers we have counts for
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Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices
Marco Bertola, Dmitry Korotkin, Ramtin Sasani
We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szegő…
Rationally weighted Hurwitz numbers, Meijer -functions and matrix integrals
M. Bertola, J. Harnad
The quantum spectral curve equation associated to KP -functions of hypergeometric type serving as generating functions for rationally weighted Hurwitz numbers is solved by gener…
Generating weighted Hurwitz numbers
M. Bertola, J. Harnad, B. Runov
Multicurrent correlators associated to KP -functions of hypergeometric type are used as generating functions for weighted Hurwitz numbers. These are expressed as formal Taylor s…
The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon
Marco Bertola, Mattia Cafasso
We show that the Kontsevich integral on matrices () is the isomonodromic tau function associated to a Riemann--Hilbert problem. The approach allo…
The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation
M. Bertola, M. Cafasso
We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy-Widom distribution, while the numerator is…
The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach
M. Bertola, M. Cafasso
We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann--Hilbert approach (different from the standard one) whereby the asymptotic analysis for larg…