160 citations · 1.4k across the 97 of their papers we have counts for
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Functional relations for higher-order free cumulants
Gaëtan Borot, Séverin Charbonnier, Elba Garcia-Failde +2
We establish the functional relations between generating series of higher-order free cumulants and moments in higher-order free probability, solving an open problem posed fifteen y…
A conjectural formula for
Alexandr Buryak, Francisco Hernández Iglesias, Sergey Shadrin
We propose a conjectural formula for and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named…
Generalised ordinary vs fully simple duality for -point functions and a proof of the Borot--Garcia-Failde conjecture
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian +1
We study a duality for the -point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for t…
Bi-Hamiltonian recursion, Liu-Pandharipande relations, and vanishing terms of the second Dubrovin-Zhang bracket
Francisco Hernández Iglesias, Sergey Shadrin
The Dubrovin-Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubr…
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
Alexander Alexandrov, Sergey Shadrin
In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we const…