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Quantization of classical spectral curves via topological recursion
Bertrand Eynard, Elba Garcia-Failde, Olivier Marchal +1
We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles.…
Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion
Olivier Marchal, Nicolas Orantin
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper…
Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: the case
Olivier Marchal, Nicolas Orantin
In this paper, we show that it is always possible to deform a differential equation with by introducing a sm…
Application de la récurrence topologique aux intégrales de matrices aléatoires et aux systèmes intégrables
Olivier Marchal
The goal of this "Habilitation à diriger des recherches" is to present two different applications, namely computations of certain partition functions in probability and application…
WKB solutions of difference equations and reconstruction by the topological recursion
Olivier Marchal
The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a -difference equation: $Ψ(x+\hbar)=\left(e…
Asymptotic expansions of some Toeplitz determinants via the topological recursion
Olivier Marchal
In this article, we study the large asymptotic expansions of Toeplitz determinants whose symbols are indicator functions of unions of arc-intervals of the unit circ…