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In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the…
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics $P(s)\propto \exp(-A s^{2-\gamma })$ for $s\gg \av{s}\equiv 1$ which is universal and intermediate between the…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this paper, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
We study the response to an external perturbation of the energy levels of a disordered metallic particle, by means of the Brownian-motion model introduced by Dyson in the theory of random matrices, and reproduce the results of a recent…
We report a systematic and detailed numerical study of statistics of the reflection coefficient $(|R(L)|^2)$ and its associated phase ($\theta$) for a plane wave reflected from a one-dimensional (1D) disordered medium beyond the random…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
In this article we study the problem of localization of eigenvalues for the non-homogeneous hierarchical Anderson model. More specifically, given the hierarchical Anderson model with spectral dimension $0<d<1$ with a random potential acting…
We analyze the nearest neighbor spacing distributions of low-lying 2+ levels of even-even nuclei. We grouped the nuclei into classes defined by the quadrupole deformation parameter (Beta2). We calculate the nearest neighbor spacing…
We investigate clustering properties of dark matter halos and galaxies to search for optimal statistics and scales where possible departures from general relativity (GR) could be found. We use large N-body cosmological simulations to…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with…
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new…
Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…