Related papers: Discrete scale invariance, and its logarithmic ext…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
We illustrate the interplay between certain discrete and continuous problems, by presenting a method for the study of the asymptotics of a divergent sequence, through consideration of the asymptotics of its continuous analogue
The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…
We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the…
In general, for single field, the scale invariant spectrum of curvature perturbation can be given by either its constant mode or its increasing mode. We show that during slowly expanding or contracting, the spectrum of curvature…
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
Scale invariant theories which contain (in $4-D$) a four index field strength are considered. The integration of the equations of motion of these $4-index$ field strength gives rise to scale symmetry breaking. The phenomena of mass…
We numerically investigate the impact of scale evolution on double parton distributions, which are needed to compute multiple hard scattering processes. Assuming correlations between longitudinal and transverse variables or between the…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.
The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…
Using the mechanism of spontaneous symmetry breaking of scale invariance obtained from the dynamics of maximal rank field strengths, it is possible to spontaneously generate confining behavior. Introducing a dilaton field, the study of non…
Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling…