Related papers: RG Equations from Whitham Hierarchy
We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly…
This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder,…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
In this article we investigate mathematically the variant of post-Newtonian mechanics using generalized fractional derivatives. The relativistic-covariant generalization of the classical equations for gravitational field is studied. The…
We refine a recent heuristic developed by Keating and the second author. Our improvement leads to a new integral expression for the conjectured asymptotic formula for shifted moments of the Riemann zeta-function. This expression is…
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns out to be e.g. the ordinary Yang-Mills theory, the G/G gauged WZNW model or the Poisson $\sigma$-model that…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We study higher derivative extension of the functional renormalization group (FRG). We consider FRG equations for a scalar field that consist of terms with higher functional derivatives of the effective action and arbitrary cutoff…
We develop an algorithmic, system-specific renormalization group (RG) procedure that is adapted from model reductions techniques from engineering control theory. The resulting "generalized" RG is a consistent generalization of the Wilsonian…
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e. locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as…
We investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the Riemann zeta-function on the critical…
Hierarchical renormalization group (RG) transformations are related to nonassociative algebras. These algebras serve as a new basic tool for a rigorous treatment of global RG flows and the search of nontrivial infrared fixed points.…
We introduce the notion of a random matrix-valued multiplicative function, generalizing Rademacher random multiplicative functions to matrices. We provide an asymptotic for the second moment based on a linear recurrence property for…
We study two types of regularizations of the determinant of Laplacian on Riemann manifold from the viewpoint of resurgence theory. One is the formal logarithmic derivative of the determinant, and the other is its exponential deformation.…