Related papers: Renormalization prescriptions and bootstrap in eff…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…
The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum…
Nonperturbative renormalization and explicit construction of the effective potential of the Hartree approximation of the two-particle-irreducible formalism are carried out in an inhomogeneous field configuration describing a uniform…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
The general prescription for constructing the continuum limit of a field theory is introduced. We then apply the prescription to construct the O(N) non-linear sigma model and the Gross-Neveu model in three dimensions using the large N…
We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection…
Chiral Effective Field Theory ($\chi$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary…
In this work, we pursue further consequences of a general formalism for non-covariant gauges developed in an earlier work (hep-th/0205042). We carry out further analysis of the additional restrictions on renormalizations noted in that work.…
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…
We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree $d$. We then conclude that orbits of renormalization are asymptotic to…
We address the problem of prescribing an optimal decision in a framework where the cost function depends on uncertain problem parameters that need to be learned from data. Earlier work proposed prescriptive formulations based on supervised…
We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…