相关论文: Distributions of Angles in Random Packing on Spher…

We consider $n$ independent random points uniformly distributed in the $d_n$-dimensional unit cube and study Pareto points, that is, points that do not coordinatewise dominate any other point. We identify the critical growth rate of $d_n$…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…

For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$,…

In this paper we study the behavior of maximum out/in-degree of binomial/Poisson random scaled sector graphs in the presence of random vertex and edge faults. We prove that the probability distribution of maximum degrees for random faulty…

We study random, finite-dimensional, ungraded chain complexes over a finite field and show that for a uniformly distributed differential a complex has the smallest possible homology with the highest probability: either zero or…

This is an extended version of the thesis presented to the Programa de P\'os-Gradua\c{c}\~ao em Matem\'atica of the Departamento de Matem\'atica, PUC-Rio, in September 2013, incorporating some suggestions from the examining commission.…

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a…

In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…

We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane $\mathbb{H}$. The angles of lattice points arising from the orbit of the modular group $PSL_{2}(\mathbb{Z})$, and lying on hyperbolic…

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$. Under various assumptions we establish the…

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…

We prove some "high probability" results on the expected value of the mean width for random perturbations of random polytopes. The random perturbations are considered for Gaussian and $p$-stable random vectors, as well as uniform…

The entropy per coordinate in a log-concave random vector of any dimension with given density at the mode is shown to have a range of just 1. Uniform distributions on convex bodies are at the lower end of this range, the distribution with…

In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tangent. We show that the expected value of the corresponding…

We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…

We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…

We consider ensembles of random polynomials of the form $p(z)=\sum_{j = 1}^N a_j P_j$ where $\{a_j\}$ are independent complex normal random variables and where $\{P_j\}$ are the orthonormal polynomials on the boundary of a bounded simply…