Results 31 to 40 of about 544 (135)

Edge Density Expansions for the Classical Gaussian and Laguerre Ensembles

Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.
ABSTRACT Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of the Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes: orthogonal,
Peter J. Forrester, Anas A. Rahman, Bo‐Jian Shen   +2 more
wiley   +1 more source

The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

Учёные записки Казанского университета: Серия Физико-математические науки
This article analyzes the inhomogeneous Hilbert boundary value problem for an upper half-plane with the finite index and boundary condition on the real axis for one generalized Cauchy–Riemann equation with a singular point on the real axis.
P. L. Shabalin, R. R. Faizov
doaj   +1 more source

Weyl metrics and Wiener-Hopf factorization

Journal of High Energy Physics, 2020
We consider the Riemann-Hilbert factorization approach to the construction of Weyl metrics in four space-time dimensions. We present, for the first time, a rigorous proof of the remarkable fact that the canonical Wiener-Hopf factorization of a matrix ...
P. Aniceto, M.C. Câmara, G.L. Cardoso, M. Rosselló   +3 more
doaj   +1 more source

Sharp Upper Bound for Amplitudes of Finite‐Gap Solutions of the Modified Korteweg‐de Vries Equation

Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.
ABSTRACT A sharp upper bound is established for the amplitudes of finite‐gap solutions of the focusing modified Korteweg–de Vries equation. The proof shows that the optimization can be carried out entirely within the finite‐dimensional hierarchy, without explicit integration of the finite‐gap solution. The maximal amplitude is expressed in terms of the
Otis C. Wright III
wiley   +1 more source

The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation [PDF]

Opuscula Mathematica, 2017
The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) is treated by the Riemann-Hilbert approach to
Dmitry Shepelsky, Lech Zielinski
doaj   +1 more source

The Huang–Yang Formula for the Low‐Density Fermi Gas: Upper Bound

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1919-1972, August 2026.
ABSTRACT We study the ground state energy of a gas of spin 1/2$1/2$ fermions with repulsive short‐range interactions. We derive an upper bound that agrees, at low density ϱ$\varrho$, with the Huang–Yang conjecture. The latter captures the first three terms in an asymptotic low‐density expansion, and in particular the Huang–Yang correction term of order
Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam, Robert Seiringer   +3 more
wiley   +1 more source

Null octagon from Deift-Zhou steepest descent

Nuclear Physics B, 2022
A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by the square of the Fredholm determinant of a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives in terms of a
A.V. Belitsky
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

The asymptotic Mahler measure of Gaussian periods

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We construct a sequence of cyclotomic integers (Gaussian periods) of particularly small Mahler measure/height. We study the asymptotics of their Mahler measure as a function of their conductor, to find that the growth rate is the (multivariate) Mahler measure of a family of log Calabi–Yau varieties of increasing dimension.
Gunther Cornelissen, David Hokken, Berend Ringeling   +2 more
wiley   +1 more source

Well-posedness of discontinuous boundary-value problems for nonlinear elliptic complex equations in multiply connected domains

Electronic Journal of Differential Equations, 2013
In the first part of this article, we study a discontinuous Riemann-Hilbert problem for nonlinear uniformly elliptic complex equations of first order in multiply connected domains. First we show its well-posedness. Then we give the representation of
Guo-Chun Wen
doaj