2 citations · 3 across the 10 of their papers we have counts for
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Asymptotics of Polynomials Orthogonal With Respect to a Generalized Freud Weight With Application to Special Function Solutions of Painlevé-IV
Ahmad Barhoumi
We obtain asymptotics of polynomials satisfying the orthogonality relations $$ \int_{\mathbb{R}} z^k P_n(z; t , N) \mathrm{e}^{-N \left(\frac{1}{4}z^4 + \frac{t}{2}z^2 \right)} \ma…
On Airy Solutions of P and Complex Cubic Ensemble of Random Matrices, I
Ahmad Barhoumi, Pavel Bleher, Alfredo Deaño +1
We show that the one-parameter family of special solutions of P, the second Painlevé equation, constructed from the Airy functions, as well as associated solutions of…
Painlevé-III Monodromy Maps Under the Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions
Ahmad Barhoumi, Oleg Lisovyy, Peter D. Miller +1
The third Painlevé equation in its generic form, often referred to as Painlevé-III(), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\…
Non-Hermitian Orthogonal Polynomials on a Trefoil
Ahmad B. Barhoumi, Maxim L. Yattselev
We investigate asymptotic behavior of polynomials satisfying non-Hermitian orthogonality relations where …