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Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which…
We employ an adapted version of H\"ormander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our…
We consider asymptotics of power series coefficients of rational functions of the form $1/Q$ where $Q$ is a symmetric multilinear polynomial. We review a number of such cases from the literature, chiefly concerned either with positivity of…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
We rewrite Arthur's asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients…
Growing interest in modeling large, complex networks has spurred significant research into generative graph models. Kronecker-style models (SKG and R-MAT) are often used due to their scalability and ability to mimic key properties of…
We derive first-order relativistic dissipative hydrodynamic equations (RDHEs) from relativistic Boltzmann equation (RBE) on the basis of the renormalization-group (RG) method. We introduce a macroscopic-frame vector (MFV) to specify the…
The critical behavior of a model describing phase transitions in 3D antiferromagnets with 2N-component real order parameters is studied within the renormalization-group (RG) approach. The RG functions are calculated in the three-loop order…
We examine the normal approximation of the modified likelihood root, an inferential tool from higher-order asymptotic theory, for the linear exponential and location-scale family. We show that the $r^\star$ statistic can be thought of as a…
We systematically explore the space of renormalization group flows of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant…
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This…
This article is the first of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. The results of the present article concern the asymptotic behaviour of solutions to linear systems of…
We study asymptotics of the partition function $Z_N$ of a Laguerre-type random matrix model when the matrix order $N$ tends to infinity. By using the Deift-Zhou steepest descent method for Riemann-Hilbert problems, we obtain an asymptotic…
The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…
We obtain Fisher-Hartwig asymptotics with root and jump type singularities in space-time under the law of the stationary Hermitian Ornstein-Uhlenbeck process, which serve as a dynamical generalization of earlier static results obtained by…
We study the Hamiltonian of a two-dimensional log-gas with a confining potential $V$ satisfying the weak growth assumption -- $V$ is of the same order than $2\log|x|$ near infinity -- considered by Hardy and Kuijlaars [J. Approx. Theory,…
The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial…
This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…
In this paper, we introduce a notion of expansion for groupoids, which recovers the classical notion of expander graphs by a family of pair groupoids and expanding actions in measure by transformation groupoids. We also consider an…
The strong coupling $\alpha_s$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing…