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Critical measures in the complex plane are saddle points for the logarithmic energy with external field. Their local and global structure was described by Martinez-Finkelshtein and Rakhmanov. In this paper we start the development of a theory of crit
Externí odkaz:
http://arxiv.org/abs/2207.02068
Autor:
Groot, Alan, Kuijlaars, Arno B. J.
Publikováno v:
Constructive Approximation 55 (2022), 775--827
In this paper, we study a class of matrix-valued orthogonal polynomials (MVOPs) that are related to 2-periodic lozenge tilings of a hexagon. The general model depends on many parameters. In the cases of constant and $2$-periodic parameter values we s
Externí odkaz:
http://arxiv.org/abs/2104.14822
Autor:
Bertola, Marco1,2 (AUTHOR), Groot, Alan3 (AUTHOR), Kuijlaars, Arno B. J.3 (AUTHOR) arno.kuijlaars@kuleuven.be
Publikováno v:
Communications in Mathematical Physics. Nov2023, Vol. 404 Issue 1, p51-95. 45p.
We show that fine domains in $\mathbf{C}$ with the property that they are Euclidean $F_\sigma$ and $G_\delta$, are in fact fine domains of existence for finely holomorphic functions. Moreover \emph{regular} fine domains are also fine domains of exist
Externí odkaz:
http://arxiv.org/abs/1706.02498
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