Related papers: Multifractal analysis of measures arising from ran…
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…
We extend the study of the multifractal analysis of the class of equicontractive self-similar measures of finite type to the non-equicontractive setting. Although stronger than the weak separation condition, the finite type property…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
We prove that, in the Baire category sense, a typical measure supported by a compact set admits a linear lower singularity spectrum. We investigate the same question for the upper singularity spectrum and for other forms of genericity.
Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…
The decoherence of quantum fluctuations into classical perturbations during inflation is discussed. A simple quantum mechanical argument, using a spatial particle wavefunction rather than a field description, shows that observable…
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…
The paper studies multifractal random measures on the sphere $\mathbb{S}^d$ constructed via multifractal products of random fields. It presents new limit theorems for multifractal products of spherical fields and conditions for the…
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a Markov process. We show that a Rauzy fractal can be…
The random local mixture of a family of primitive substitution rules with noble mean inflation multiplier is investigated. This extends the random Fibonacci example that was introduced by Godr\`{e}che and Luck in 1989. We discuss the…
By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock…
We re-formulate rotation measure (RM) synthesis for data sets with discrete frequency channels and an arbitrary channel response function. The most commonly used version of the formalism by Brentjens & De Bruyn assumes a top-hat response…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
The multifractal formalism characterizes the scaling properties of a physical density rho as a function of the distance L. To each singularity alpha of the field is attributed a fractal dimension for its support f(alpha). An alternative…
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found…
Negative, or latent, dimensions have always attracted a strong interest since their discovery. When randomness is introduced in multifractals, the sample-to-sample fluctuations of multifractal spectra emerge inevitably, which has motivated…
We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…
We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we…