Related papers: A note on the renormalization group approach to th…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
The explicit one-loop renormalizability of pure Yang-Mills theory with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization as the required counter terms are consistent with a single re-scaling of…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
The non-commutative Central Limit Theorem (CLT) introduced by Speicher in 1992 states that given almost any sequence of non-commutative random variables that commute or anti-commute pair-wise, the *-moments of the normalized partial sum…
The coupled cluster method (CCM) is one of the most successful and universally applicable techniques in quantum many-body theory. The intrinsic nonlinear and non-perturbative nature of the method is considered to be one of its advantages.…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
The second and third-named authors (arXiv:1705.04115) established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was adapted to families of elliptic curves in by the first and…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the…
In this paper, we provide general central limit theorems (CLT's) for associated random variables (rv's) following the approaches used by Newman (1980) and Olivera et al.(2012). Given some assumptions, a Lyapounov-Feller-Levy type theorem is…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
We prove a central limit theorem (CLT) for the Frechet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Frechet mean is unique. Previous general CLT results in this…
The stability of the Luttinger liquid to small transverse hopping has been studied from several points of view. The renormalization group approach in particular has been criticized because it does not take explicitly into account the…
We establish the central limit theorem for the number of groups at the equilibrium of a coagulation-fragmentation process given by a parameter function with polynomial rate of growth. The result obtained is compared with the one for random…
We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders we illustrate the…
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…
This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique…
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the renormalization group running scale are…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…