Related papers: Multifractal analysis of complex random cascades
The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate…
We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
Multifractal analysis is a powerful approach for characterizing ergodic or localized nature of eigenstates in complex quantum systems. In this context, the eigenvectors of random matrices belonging to invariant ensembles naturally serve as…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…
We present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The approach is based on the chaos representation property and…
We investigate a zero-range process where the underlying one-particle stationary distribution has multifractality. The multiparticle stationary probability measure can be written in a factorized form. If the number of the particles is…
We consider a self-similar phase space with specific fractal dimension $d$ being distributed with spectrum function $f(d)$. Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Any Borel probability measure supported on a Cantor set of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…