Broadly speaking, I am interested in asymptotic analysis, approximation theory, special function theory, and their application to problems in mathematical physics and random matrix theory. One of the main tools I use is the Riemann-Hilbert problem; for a nice introduction to the method as it applies to integrable systems, see Alexander Its' Notices article.
Below you will find some of my published papers as well as some preprints. If you have trouble accessing any of these publications, please let me know and I'll be happy to share a preprint! Many (but not necessarily all) of my preprints are also available on the arxiv.
A. Barhoumi, O. Lisovyy, P. Miller, and A. Prokhorov. Painlevé-III Monodromy Maps Under the D6→D8 Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions. In Review. arXiv:2307.11217.
Work Submitted or in Preparation
A. Barhoumi, P. Bleher, A. Deaño, and M. Yattselev. On Airy solutions of PII and complex cubic ensemble of random matrices, I. Submitted [PDF].
A. Barhoumi, P. Bleher, A. Deaño, and M. Yattselev. On Airy solutions of PII and complex cubic ensemble of random matrices, II. In preparation.
A. Barhoumi, P. Bleher, R. Gharakhloo, and K. T-R. McLaughlin. Topological Expansion in the Complex Quartic Random Matrix Model: Two-cut Case. In preparation.