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6 papers · 2 filters
The factorial growth of topological recursion
Gaëtan Borot, Bertrand Eynard, Alessandro Giacchetto
We show that the -point, genus- correlation functions of topological recursion on any regular spectral curve with simple ramifications grow at most like as $g…
Equilibrium of Charges and Differential Equations Solved by Polynomials II
Igor Loutsenko, Oksana Yermolayeva
We continue study of equilibrium of two species of 2d coulomb charges (or point vortices in 2d ideal fluid) started in (Igor Loutsenko, J. Phys. A: Math. Gen. 37, 1309, 2004). Alth…
A -version of the relation between the hypercube, the Krawtchouk chain and Dicke states
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
It is shown how the spin chain based on the dual -Krawtchouk polynomials is connected to a weighted hypercube through the use of -Dicke states. The representation theoretic u…
The Steklov problem for exterior domains: asymptotic behavior and applications
Denis S. Grebenkov, Adrien Chaigneau
We investigate the spectral properties of the Steklov problem for the modified Helmholtz equation in the exterior of a compact set, for which the positive parameter $…
Meta Algebras and Biorthogonal Rational Functions: The Hahn Case
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated met…
Vortices and Factorization
Igor Loutsenko, Oksana Yermolayeva
We review applications of factorization methods to the problem of finding stationary point vortex patterns in two-dimensional fluid mechanics. Then we present a new class of patter…