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pro vyhledávání: '"Dzhamay, Anton"'
In this paper we consider two examples of certain recurrence relations, or nonlinear discrete dynamical systems, that appear in the theory of orthogonal polynomials, from the point of view of Sakai's geometric theory of Painlev\'e equations. On one h
Externí odkaz:
http://arxiv.org/abs/2202.11263
Publikováno v:
In Journal of Differential Equations 5 August 2024 399:281-334
In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlev\'e equations using the geometric framework of the Okamoto Space of Initial Cond
Externí odkaz:
http://arxiv.org/abs/2109.06968
Publikováno v:
Journal of Differential Equations, Volume 399, 5 August 2024, Pages 281-334
It is well-known that differential Painlev\'e equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique -- there are many very different Hamiltonians that result in the same differential Pain
Externí odkaz:
http://arxiv.org/abs/2109.06428
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 1--18; 354003
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 theory of Painlev\'e equations. On one hand, this gives us one more det
Externí odkaz:
http://arxiv.org/abs/2001.00494
Over the last decade it has become clear that discrete Painlev\'e equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing a given non-autonomous recurrence as a discrete Painlev\'e equation
Externí odkaz:
http://arxiv.org/abs/1910.10981
Autor:
Dzhamay, Anton, Knizel, Alisa
The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlev\'e equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval g
Externí odkaz:
http://arxiv.org/abs/1903.06159
Autor:
Dzhamay, Anton, Takenawa, Tomoyuki
Publikováno v:
SIGMA 14 (2018), 075, 20 pages
Although the theory of discrete Painlev\'e (dP) equations is rather young, more and more examples of such equations appear in interesting and important applications. Thus, it is essential to be able to recognize these equations, to be able to identif
Externí odkaz:
http://arxiv.org/abs/1804.10341
It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel-Roberts-Thompson mappings, can be deautonomized to discrete Painlev\'e equations. However, the dependence of this procedure on the choice of a p
Externí odkaz:
http://arxiv.org/abs/1702.04907
Publikováno v:
In Applied Mathematics Letters October 2021 120