Related papers: Selfsimilar random fractal measure using contracti…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions. Singularity of measures brings difficulties in (especially non-linear) analysis on fractals. In this paper, we…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We show that if a discrete random measure on the unit ball of a separable Hilbert space satisfies the Ghirlanda-Guerra identities then by randomly deleting half of the points and renormalizing the weights of the remaining points we obtain…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
In this paper, we construct and then prove the up-to constants uniqueness of the natural measure on several random fractals, namely the SLE cut points, SLE boundary touching points, CLE pivotal points and the CLE carpet/gasket. As an…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…
We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
A new kind of composite were manufactured by densification of co-crumpled aluminium and tantalum thin foils using close die compression. It was shown by optical micrography that its microstructure is highly interlocked. The morphology was…