Related papers: Counting nodal domains
We study directly the length of the domain walls (DW) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and Gaussian bond…
We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…
Current astrophysical models of the interstellar medium assume that small scale variation and noise can be modelled as Gaussian random fields or simple transformations thereof, such as lognormal. We use topological methods to investigate…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…
We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin…
We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give…
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results…
When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…
We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
We discuss the statistical properties of the volume of the nodal set of wave function for two paradigmatic model systems which we consider in arbitrary dimension $s\ge 2$: the cuboid as a paradigm for a regular shape with separable wave…
The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
In this work, which is the first part of a series of two papers, we study the random walk loop soup in dimension two. More specifically, we estimate the probability that two large connected components of loops come close to each other, in…
This is a report on the derivation and application of a generalized version of the Wulff construction in two dimensions. The construction is used to find the shape of a domain containing an XY-like order parameter. In such a domain the…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radius $R$ is proportional to $\pi R^2$ in the large $R$ limit.…