Null octagon from Deift-Zhou steepest descent
نویسندگان
چکیده
A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by square Fredholm determinant a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives terms two-dimensional Riemann-Hilbert problem. We solve latter null limit making use Deift-Zhou steepest descent. reproduce exact octagonal anomalous dimension 't Hooft coupling and provide novel formulation as convolution non-linear quasiclassical phase with Fermi distribution infinite chemical potential.
منابع مشابه
Steepest Descent
The steepest descent method has a rich history and is one of the simplest and best known methods for minimizing a function. While the method is not commonly used in practice due to its slow convergence rate, understanding the convergence properties of this method can lead to a better understanding of many of the more sophisticated optimization methods. Here, we give a short introduction and dis...
متن کاملApproximate Steepest Coordinate Descent
We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach the efficiency of steepest coordinate descent (SCD), enabling an acceleration of a factor of up to n, the number of coordinates. In many practical applicatio...
متن کاملSteepest descent on factor graphs
x f(x, θ) log f(x, θ) exists for all θ and θ. In principle, one can apply the sum-product algorithm in order to find (1), which involves the following two steps [2]: 1. Determine f(θ) by sum-product message passing. 2. Maximization step: compute θmax △ = argmaxθ f(θ). This procedure is often not feasible, since • When the variable x is continuous, the sum-product rule may lead to intractable in...
متن کاملMann-type Steepest-descent and Modified Hybrid Steepest-descent Methods for Variational Inequalities in Banach Spaces
1Department of Mathematics, Shanghai Normal University, Shanghai; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China 2Department of Mathematics & Statistics, College of Science, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; and Department of Mathematics, Aligarh Muslim University, Aligarh, India 3Department of Applied Mathematics, National S...
متن کاملOn Spectral Properties of Steepest Descent Methods
In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian matrix. On the other hand, the convergence of the classical Cauchy stee...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nuclear Physics B
سال: 2022
ISSN: ['1873-1562', '0550-3213']
DOI: https://doi.org/10.1016/j.nuclphysb.2022.115844