23 citations · 105 across the 17 of their papers we have counts for
5 papers · 1 filter
Sums of Random Matrices and the Potts Model on Random Planar Maps
Max R. Atkin, Benjamin Niedner, John F. Wheater
We compute the partition function of the -states Potts model on a random planar lattice with allowed, equally weighted colours on a connected boundary. To this end, we…
Boundary States of the Potts Model on Random Planar Maps
Max Atkin, Benjamin Niedner, John Wheater
We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on…
A Riemann-Hilbert problem for equations of Painlevé type in the one matrix model with semi-classical potential
Max R. Atkin
We study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a…
The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models
Max R. Atkin
We review some aspects of recent work concerning double scaling limits of singularly perturbed hermitian random matrix models and their connection to Painlevé equations. We present…
Random matrix ensembles with singularities and a hierarchy of Painlevé III equations
Max R. Atkin, Tom Claeys, Francesco Mezzadri
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaussian Unitary Ensem…