latex, 1 figure, 55 pagesWe compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations
For the description of closed as well as open two-dimensional Hamiltonian systems with mixed phase-...
We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and b...
The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on th...
latex, 1 figure, 55 pagesWe compute the mixed correlation function in a way which involves only the ...
37 pages, latexWe compute expectation values of mixed traces containing both matrices in a two matri...
review article, Latex, 139 pages, many figures.We review the method of symplectic invariants recentl...
AbstractWe consider the biorthogonal polynomials associated to the two-matrix model where the eigenv...
In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer clus...
International audienceWe write the loop equations for the $\beta$ two-matrix model, and we propose a...
International audienceWe write the loop equations for the β two-matrix model, and we propose a topol...
Latex, 31 pages, 20 figures; few misprints corrected.We compute the complete topological expansion o...
In this paper we complement our recent result on the explicit formula for the planar limit of the fr...
138 pages, based on lectures by Bertrand Eynard at IPhT, SaclayWe provide a self-contained introduct...
Includes bibliographical references (leaf [59]).The spectral function associated with the Sturm-Liou...
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in ...
For the description of closed as well as open two-dimensional Hamiltonian systems with mixed phase-...
We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and b...
The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on th...
latex, 1 figure, 55 pagesWe compute the mixed correlation function in a way which involves only the ...
37 pages, latexWe compute expectation values of mixed traces containing both matrices in a two matri...
review article, Latex, 139 pages, many figures.We review the method of symplectic invariants recentl...
AbstractWe consider the biorthogonal polynomials associated to the two-matrix model where the eigenv...
In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer clus...
International audienceWe write the loop equations for the $\beta$ two-matrix model, and we propose a...
International audienceWe write the loop equations for the β two-matrix model, and we propose a topol...
Latex, 31 pages, 20 figures; few misprints corrected.We compute the complete topological expansion o...
In this paper we complement our recent result on the explicit formula for the planar limit of the fr...
138 pages, based on lectures by Bertrand Eynard at IPhT, SaclayWe provide a self-contained introduct...
Includes bibliographical references (leaf [59]).The spectral function associated with the Sturm-Liou...
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in ...
For the description of closed as well as open two-dimensional Hamiltonian systems with mixed phase-...
We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and b...
The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on th...