3 papers
math-ph2025
The lozenge tiling model via non-Hermitian orthogonal polynomials
Ahmad Barhoumi, Maurice Duits
We consider the 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.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, , over the interval , 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 satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $…