Related papers: Point processes and the infinite symmetric group. …
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…
We calculate the asymptotic behaviour of correlation functions as a function of the microscopic parameters for a Bose-Fermi mixture with repulsive interaction in one dimension. For two cases, namely polarized and unpolarized fermions the…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
Motivated by applications in functional data analysis, we study the partial sum process of sparsely observed, random functions. A key novelty of our analysis are bounds for the distributional distance between the limit Brownian motion and…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
We study the mutual regularity properties of Palm measures of point processes, and establish that a key determining factor for these properties is the rigidity-tolerance behaviour of the point process in question (for those processes that…
We investigate harmonic analysis of random matrices of large size with their Dyson indices going simultaneous to zero, that is in the high temperature limit. In this regime, we show that the multivariate Bessel function/Heckman-Opdam…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
The close similarity between the hierarchies of multiple-point correlation functions for the diffusion-limited coalescence and annihilation processes has caused some recent confusion, raising doubts as to whether such hierarchies uniquely…
In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
We trace with analytical methods and in a model parameter independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution, as a now standard prescription for the distribution of the…
We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…
The infinite-dimensional unitary group U(infinity) is the inductive limit of growing compact unitary groups U(N). In this paper we solve a problem of harmonic analysis on U(infinity) stated in the previous paper math/0109193. The problem…
We develop a framework of canonical correlation analysis for distribution-valued functional data within the geometry of Wasserstein spaces. Specifically, we formulate an intrinsic concept of correlation between random distributions, propose…
We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on…
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…