Related papers: Hyperuniformity in regular trees
Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
This study is about the properties of the sets of objects associated in a structure resulting from multiple-processes involving chance as are materials whose texture is unordered and random. Being a paper scientist the author refers to the…
We provide a new geometric representation of a family of fragmentation processes by nested laminations, which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation obtained by cutting a…
Heuristics indicate that point processes exhibiting clustering of points have larger critical radius $r_c$ for the percolation of their continuum percolation models than spatially homogeneous point processes. It has already been shown, and…
We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small…
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size…
We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in con- junction of the replica method used to study thermodynamics properties of disordered…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
Consider non-intersecting Brownian motions on the line leaving from the origin and forced to two arbitrary points. Letting the number of Brownian particles tend to infinity, and upon rescaling, there is a point of bifurcation, where the…