Asymptotic properties of special function solutions of the Painlevé-III equation for fixed parameters
H. Pan · A. Prokhorov
Postdoctoral Fellow · Baylor University
Andrei
Prokhorov
I study integrable systems and asymptotic phenomena at the intersection of analysis, probability, and mathematical physics.
Ψ+(z) = Ψ−(z) J(z)
ℂ
q″ = 2q³ + tq + α
Scroll to discover ↓
01 — Research
Structure within
complexity.
My research uses Riemann–Hilbert methods to reveal precise asymptotic behavior in nonlinear differential equations and probability models.
These methods connect integrable systems, special functions, random matrix theory, and universality—turning complicated analytic questions into geometric ones.
01Riemann–Hilbert problems02Painlevé equations03Random matrices04Integrable probability05Asymptotic analysis
02 — Selected work
List of publications
↗
Nonlinear steepest descent on a torus: A case study of the Landau–Lifshitz equation
H. Desiraju · A. R. Its · A. Prokhorov
Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus
H. Desiraju · P. Ghosal · A. Prokhorov
Painlevé-III monodromy maps under the D₆ → D₈ confluence
A. Barhoumi · O. Lisovyy · P. D. Miller · A. Prokhorov
Differential equations for the KPZ and periodic KPZ fixed points
J. Baik · A. Prokhorov · G. L. F. Silva
On β = 6 Tracy–Widom distribution and the second Calogero–Painlevé system
A. R. Its · A. Prokhorov
Mixed moments of characteristic polynomials of random unitary matrices
E. C. Bailey · S. Bettin · G. Blower · J. B. Conrey · A. Prokhorov · M. O. Rubinstein · N. C. Snaith
Connection problem for Painlevé tau functions
A. Prokhorov
On the analysis of incomplete spectra in random matrix theory
T. Bothner · A. R. Its · A. Prokhorov
On some Hamiltonian properties of the isomonodromic tau functions
A. R. Its · A. Prokhorov
Monodromy dependence and connection formulae for isomonodromic tau functions
A. R. Its · O. Lisovyy · A. Prokhorov
The Maxwell operator with periodic coefficients in a cylinder
A. Prokhorov · N. Filonov
Connection problem for the tau-function of the Sine–Gordon reduction of Painlevé-III
A. R. Its · A. Prokhorov
Regularity of electromagnetic fields in convex domains
A. Prokhorov · N. Filonov
03 — Teaching & talks
Mathematics is a
shared language.
I enjoy helping students move from computation to insight. My teaching spans calculus, differential equations, Fourier analysis, numerical methods, and partial differential equations.
CalculusDifferential equationsFourier analysisNumerical methods
Selected presentations
Apr 20–24, 2026The Kardar–Parisi–Zhang Universality Class & Related Topics · Brin Mathematics Research Center ↗
Left Tail Asymptotics of the Two-Point Distribution of the Airy Process
Feb 4, 2026Departmental Colloquium · Baylor University
Painlevé equations and their generalizations
Connection formulas for the Heun equation from Painlevé theory
Presentation archive
Slides, posters & recorded talks
9 topics · 2015–2025
Nonlinear steepest descent on a torus
IMACS Conference & University of South Florida · 2025
Painlevé-III monodromy maps under the D₆ → D₈ confluence
Midwestern Workshop & IMACS · 2022
Differential equations for the KPZ and periodic KPZ fixed points
SIAM NWCS & MSRI · 2021–2022
Riemann–Hilbert problems in random matrix theory
MSRI mini-course · 2021
Connection problem for Painlevé tau functions
Miami University & dissertation defense · 2019
Hamiltonian properties of isomonodromic tau functions
BIRS & Midwestern Workshop · 2018
Incomplete spectra in random matrix theory
University of Virginia & Midwestern Workshop · 2017
Monodromy dependence and connection formulae
Cargèse · 2016
Sine–Gordon reduction of Painlevé-III
CRM Montréal · 2015–2016
04 — Community & outreach
Mathematics grows
through exchange.
Collaborations, seminars, summer schools, and outreach are an essential part of my mathematical work.
Research network
Selected activities
05 — Contact
Let’s discuss
mathematics.
Department of Mathematics
Baylor University
Sid Richardson 328
1410 S. 4th Street
Waco, TX 76706