Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Evolution Equations, Exactly Solvable Models and Random Matrices in honor of Alexander Its' 70th birthday

The Guest Editors for this special issue are

Thomas Bothner (University of Bristol, UK)
Tamara Grava (University of Bristol, UK)
Ken McLaughlin (Tulane University, New Orleans, USA)
Andrei Prokhorov (University of Michigan, Ann Arbor, USA)

This special issue is dedicated to the 70th birthday of Alexander Its and aims to honor his many groundbreaking contributions to the theory of integrable systems over the past 40 years. In particular, topics for this issue include:

  • nonlinear evolution equations, inverse scattering theory, unified transform method, algebro-geometric methods;
  • isomonodromy deformation method, tau functions, Painlevé equations;
  • exactly solvable models, quantum integrable systems, correlation functions, operator determinants;
  • random matrices, orthogonal polynomials, universality, interacting particle systems, beta-ensembles.
This issue is related to the conference in honor of Alexander's 70th birthday to be held at the University of Bristol, September 12–16, 2022.

There is no limit to the length of an article. Deadline for paper submission is December 31, 2023.

How to Submit an Article to the Issue.

All articles will go through the standard peer reviewing procedure of SIGMA.

Papers in this Issue:

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 and Andrei Prokhorov
SIGMA 20 (2024), 019, 77 pages   [ abs   pdf ]
Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III $({\rm D}_7)$ Equation
Robert J. Buckingham and Peter D. Miller
SIGMA 20 (2024), 008, 27 pages   [ abs   pdf ]
Computing the Tracy-Widom Distribution for Arbitrary $\beta>0$
Thomas Trogdon and Yiting Zhang
SIGMA 20 (2024), 005, 26 pages   [ abs   pdf ]
Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function
Percy Deift and Mateusz Piorkowski
SIGMA 20 (2024), 004, 48 pages   [ abs   pdf ]
Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices
Marco Bertola, Dmitry Korotkin and Ramtin Sasani
SIGMA 19 (2023), 104, 22 pages   [ abs   pdf ]
Jacobi Beta Ensemble and $b$-Hurwitz Numbers
Giulio Ruzza
SIGMA 19 (2023), 100, 18 pages   [ abs   pdf ]
Exact Correlations in Topological Quantum Chains
Nick G. Jones and Ruben Verresen
SIGMA 19 (2023), 098, 54 pages   [ abs   pdf ]
Spherical Induced Ensembles with Symplectic Symmetry
Sung-Soo Byun and Peter J. Forrester
SIGMA 19 (2023), 033, 28 pages   [ abs   pdf ]
Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
Thomas Chouteau and Sofia Tarricone
SIGMA 19 (2023), 030, 30 pages   [ abs   pdf ]
Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials
Sergey Berezin, Arno B.J. Kuijlaars and Iván Parra
SIGMA 19 (2023), 020, 18 pages   [ abs   pdf ]

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