Related papers: Renormalization Group and Stochastic PDE's
We apply Renormalization Group (RG) techniques to Classical Information Theory, in the limit of large codeword size $n$. In particular, we apply RG techniques to (1) noiseless coding (i.e., a coding used for compression) and (2) noisy…
Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish…
In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…
we investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the…
The renormalization of the periodic potential is investigated in the framework of the Euclidean one-component scalar field theory by means of the differential RG approach. Some known results about the sine-Gordon model are recovered in an…
We study perturbative Wilsonian renormalisation group (RG) for the scalar $\phi^4$ theory at finite temperature to one loop order in the Schwinger-Keldysh closed-time-path (CTP) formalism. By explicitly integrating out the UV modes, we show…
In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function…
The effective potential $V$ is considered in massless $\lambda\phi^4_4$ theory. The expansion of $V$ in powers of the coupling $\lambda$ and of the logarithm of the background field $\phi$ is reorganized in two ways; first as a series in…
We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…
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…
We prove local existence of solutions for a class of suitably renormalised coupled SPDE-ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh-Nagumo system…
We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic…
This paper is devoted to presenting in detail the non-perturbative renormalization group (NPRG) formalism to investigate out-of-equilibrium systems and critical dynamics in statistical physics. The general NPRG framework for studying…
We construct global-in-time singular dynamics for the (renormalized) cubic fourth order nonlinear Schr\"odinger equation on the circle, having the white noise measure as an invariant measure. For this purpose, we introduce the…
We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to…
The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…
The nonrelativistic reduction of the self-consistent covariant density functional theory is realized for the first time with the similarity renormalization group (SRG) method. The reduced nonrelativistic Hamiltonian and densities are…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.}…