A. Barhoumi

activity

20192026

most citedStrong Asymptotics of Jacobi-Type Kissing Polynomials

2 citations · 3 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2026

Universal Asymptotics and Exact Enumeration of Eulerian Maps

Ahmad Barhoumi, Roozbeh Gharakhloo, Nathan Hayford

We calculate the asymptotics of the number of connected, labeled, genus $g$ Eulerian maps with an arbitrary degree sequence, in the limit as the total number of vertices tends to i…

math-ph2025

The $q^{Volume}$ lozenge tiling model via non-Hermitian orthogonal polynomials

Ahmad Barhoumi, Maurice Duits

We consider the $q^{Volume}$ lozenge tiling model on a large, finite hexagon. It is well-known that random lozenge tilings of the hexagon correspond to a two-dimensional deter…

math-ph2024

On Airy solutions of P $_{II}$ and the complex cubic ensemble of random matrices, II

Ahmad Barhoumi, Pavel Bleher, Alfredo Deaño +1

We describe the pole-free regions of the one-parameter family of special solutions of P $_{II}$ , the second Painlevé equation, constructed from the Airy functions. This is ac…

math.CA2023

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…

math-ph2023

On Airy Solutions of P $_{II}$ 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 $_{II}$ , the second Painlevé equation, constructed from the Airy functions, as well as associated solutions of…

math.CA2023★ 1 cited

Painlevé-III Monodromy Maps Under the $D_{6} \to D_{8}$ 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( $D_{6}$ ), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\…

math.CA2023

Non-Hermitian Orthogonal Polynomials on a Trefoil

Ahmad B. Barhoumi, Maxim L. Yattselev

We investigate asymptotic behavior of polynomials $Q_{n} (z)$ satisfying non-Hermitian orthogonality relations $\int_{Δ} s^{k} Q_{n} (s) ρ (s) d s = 0, k \in {0, \dots, n - 1},$ where $Δ$ …

math-ph2022

Investigation of the two-cut phase region in the complex cubic ensemble of random matrices

Ahmad Barhoumi, Pavel M. Bleher, Alfredo Deaño +1

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 i…

math.CA2021★ 2 cited

Strong Asymptotics of Jacobi-Type Kissing Polynomials

Ahmad Barhoumi

We investigate asymptotic behavior of polynomials $p_{n}^{ω} (z)$ satisfying varying non-Hermitian orthogonality relations $$ \int_{-1}^{1} x^kp^ω_n(x)h(x) e^{\mathrm{i} ωx}\mathrm{d} x…

math.CA2020

Global Phase Portrait and Large Degree Asymptotics for the Kissing Polynomials

Ahmad Barhoumi, Andrew F. Celsus, Alfredo Deaño

We study a family of monic orthogonal polynomials which are orthogonal with respect to the varying, complex valued weight function, $exp (n sz)$ , over the interval $[- 1, 1]$ , where $…

math.CA2019

Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight

Ahmad Barhoumi, Maxim L. Yattselev

We investigate asymptotic behavior of polynomials $Q_{n} (z)$ satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $…