20 citations · 85 across the 20 of their papers we have counts for
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On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves
Anton Dzhamay, Galina Filipuk, Alexander Stokes
We consider several examples of nonautonomous systems of difference equations coming from semi-classical orthogonal polynomials via recurrence coefficients and ladder operators, wi…
Orthogonal Polynomials for the Gaussian Weight with a Jump and Discrete Painlevé Equations
Anton Dzhamay, Elizaveta Trunina
We describe a refined version of the discrete Painlevé identification problem that emphasizes the importance on going beyond just the surface type in describing a discrete Painlevé…
On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions
Anton Dzhamay
In this short note we give two examples of using the algebro-geometric theory of Painlevé equations to solve the Painlevé identification problem. The equations that we consider wer…
What is the symmetry group of a d- discrete Painlevé equation?
Anton Dzhamay, Yang Shi, Alexander Stokes +1
The symmetry group of a (discrete) Painlevé equation provides crucial information on the properties of the equation. In this paper we argue against the commonly-held belief that th…
On the recurrence coefficients for the -Laguerre weight and discrete Painlevé equations
Jie Hu, Anton Dzhamay, Yang Chen
We study the dependence of recurrence coefficients in the three-term recurrence relation for orthogonal polynomials with a certain deformation of the -Laguerre weight on the deg…
Recurrence relations for the generalized Laguerre and Charlier orthogonal polynomials and discrete Painlevé equations on the Sakai surface
Xing Li, Anton Dzhamay, Galina Filipuk +1
This paper concerns the discrete version of the Painlevé identification problem, i.e., how to recognize a certain recurrence relation as a discrete Painlevé equation. Often some cl…
Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach
Anton Dzhamay, Galina Filipuk, Adam Ligȩza +1
It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique -- there are many v…
Gap Probabilities in the Laguerre Unitary Ensemble and Discrete Painlevé Equations
Yang Chen, Anton Dzhamay, Jie Hu
In this paper we study a certain recurrence relation, that can be used to generate ladder operators for the Laguerre Unitary ensemble, from the point of view of Sakai's geometric t…
Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations
Anton Dzhamay, Galina Filipuk, Alexander Stokes
Over the last decade it has become clear that discrete Painlevé equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing…
Combinatorics of Matrix Factorizations and Integrable Systems
Anton Dzhamay
We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two element…