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pro vyhledávání: '"Barhoumi, Ahmad"'
We describe the pole-free regions of the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlev\'e equation, constructed from the Airy functions. This is achieved by exploiting the connection between these solutions and the
Externí odkaz:
http://arxiv.org/abs/2403.03023
Autor:
Barhoumi, Ahmad
We obtain asymptotics of polynomials satisfying the orthogonality relations $$ \int_{\mathbb{R}} z^k P_n(z; t , N) \mathrm{e}^{-N \left(\frac{1}{4}z^4 + \frac{t}{2}z^2 \right)} \mathrm{d} z = 0 \quad \text{ for } \quad k = 0, 1, ..., n-1, $$ where th
Externí odkaz:
http://arxiv.org/abs/2312.11294
We show that the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlev\'e equation, constructed from the Airy functions, as well as associated solutions of P$_\mathrm{XXXIV}$ and S$_\mathrm{II}$, can be expressed via the re
Externí odkaz:
http://arxiv.org/abs/2310.14898
Publikováno v:
SIGMA 20 (2024), 019, 77 pages
The third Painlev\'e equation in its generic form, often referred to as Painlev\'e-III($D_6$), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\right)^2-\frac{1}{x}\frac{{\rm d}u}{{\rm d}x}+\frac{\alpha u^2+\be
Externí odkaz:
http://arxiv.org/abs/2307.11217
We investigate asymptotic behavior of polynomials $ Q_n(z) $ satisfying non-Hermitian orthogonality relations $$ \int_\Delta s^kQ_n(s)\rho(s)ds =0, \quad k\in\{0,\ldots,n-1\}, $$ where $ \Delta $ is a Chebotar\"ev (minimal capacity) contour connectin
Externí odkaz:
http://arxiv.org/abs/2303.17037
Publikováno v:
J. Math. Phys., 63, Paper No. 063303, 2022
We investigate the phase diagram of the complex cubic unitary ensemble of random matrices with the potential $V(M)=-\frac{1}{3}M^3+tM$ where $t$ is a complex parameter. As proven in our previous paper, the whole phase space of the model, $t\in\mathbb
Externí odkaz:
http://arxiv.org/abs/2201.12871
Autor:
Barhoumi, Ahmad
Indiana University-Purdue University Indianapolis (IUPUI)
We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the com
We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the com
Externí odkaz:
https://hdl.handle.net/1805/23029
Autor:
Barhoumi, Ahmad
We investigate asymptotic behavior of polynomials $p^{\omega}_n(z)$ satisfying varying non-Hermitian orthogonality relations $$ \int_{-1}^{1} x^kp^{\omega}_n(x)h(x) e^{\mathrm{i} \omega x}\mathrm{d} x =0, \quad k\in\{0,\ldots,n-1\}, $$ where $h(x) =
Externí odkaz:
http://arxiv.org/abs/2101.04147
Autor:
Barhoumi, Ahmad B.1 (AUTHOR) barhoumi@umich.edu, Yattselev, Maxim L.2 (AUTHOR)
Publikováno v:
Constructive Approximation. Apr2024, Vol. 59 Issue 2, p271-331. 61p.
We study a family of monic orthogonal polynomials which are orthogonal with respect to the varying, complex valued weight function, $\exp(nsz)$, over the interval $[-1,1]$, where $s\in\mathbb{C}$ is arbitrary. This family of polynomials originally ap
Externí odkaz:
http://arxiv.org/abs/2008.08724