Related papers: Renormgroup Invariants and Approximations of Mappi…
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential…
The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom. What all these methods have in common -- which is what explains their success -- is that…
We investigate the generalization error of group-invariant neural networks within the Barron framework. Our analysis shows that incorporating group-invariant structures introduces a group-dependent factor $\delta_{G,\Gamma,\sigma} \le 1$…
In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations.…
We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of…
We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field. Our method is…
We describe some properties of Renormalization Group transformations. Especially we show why some of the RG transformations have redundant eigenoperators with eigenvalues that cannot be determined by simple dimensional analysis and give the…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization…
Building on the Renormalization Group (RG) method the beam-beam interaction in circular colliders is studied. A regularized symplectic RG beam-beam map, that describes successfully the long-time asymptotic behavior of the original system…
Recent advances in quantum simulator experiments enable unprecedented access to quantum many-body states through snapshot measurements of individual many-body configurations. Here, we introduce an exact renormalization group (RG)…
The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e. involving only generalized traces and product of them) and are showed to strongly…
The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or…
I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian…
Non-parametric tests based on permutation, rotation or sign-flipping are examples of group-invariance tests. These tests test invariance of the null distribution under a set of transformations that has a group structure, in the algebraic…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
The renormalization group (RG) approach is largely responsible for the considerable success that has been achieved in developing a quantitative theory of phase transitions. Physical properties emerge from spectral properties of the…