Related papers: A Short Lecture on Divergences
In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour or properties that are novel (by some salient standard). Here, my…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…
This is the text of a talk given at the conference in memory of Claude Itzykson at Saclay in June 1996. It contains an introductory survey and an account of recent developments in the field theoretic RG approach to reaction-diffusion…
These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
Transfer learning techniques are important to handle small training sets and to allow for quick generalization even from only a few examples. The following paper is the introduction as well as the literature overview part of my thesis…
We review what we have learned about the "Renormalization-Group peculiarities" which were discovered about twenty years ago by Griffiths and Pearce, and which questions they asked are still widely open. We also mention some related…
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 is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
A simple introduction of renormalization in quantum field theory is discussed. Explanation of concepts is emphasized instead of the technical details.
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.