Related papers: Renormalization of Generalized KPZ equation
We survey several results connecting combinatorics and Wronskian solutions of the KP equation, contextualizing the successes of a recent approach introduced by Kodama, et. al. We include the necessary combinatorial and analytical background…
We consider a $p$-Laplace evolution problem with stochastic forcing on a bounded domain $D\subset\mathbb{R}^d$ with homogeneous Dirichlet boundary conditions for $1<p<\infty$. The additive noise term is given by a stochastic integral in the…
The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group…
The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi,…
We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for…
We deal with a wide class of generalized nonlocal $p$-Laplace equations, so-called nonlocal $G$-Laplace equations, in the Heisenberg framework. Under natural hypotheses on the $N$-function $G$, we provide a unified approach to investigate…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
Recently Tsai et.al. (cond-mat/0406174) have used the renormalization group approach to study strong coupling superconductors without assuming a broken symmetry phase. We use the hydrodynamic formulation to study the same problem with the…
We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized…
After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the $n$-point…
The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…
In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
The study of homogenization results has long been a central focus in the field of mathematical analysis, particularly for equations without lower-order terms. However, the importance of studying homogenization results for parabolic…
A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…
Refining an earlier result due to Hahlomaa, we provide a new Carleson-type condition for $k$-regular sets in the Heisenberg group $\mathbb{H}^n$ to have big pieces of Lipschitz images of subsets of $\mathbb{R}^k$ for $1\leq k\leq n$. Our…
The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is carried out through a decomposition of the sine-Gordon field in slow and fast modes.…
The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point…