131 citations · 233 across the 25 of their papers we have counts for
32 papers
Point process convergence of large inradii of Poisson-Laguerre tessellations
Matthias Schulte, Martina Švarc Petráková
In this paper we study a weighted generalization of the Poisson-Voronoi tessellation called the Poisson-Laguerre tessellation, where the nuclei of the generating Poisson process ad…
First passage percolation on Erdős-Rényi graphs with general weights
Fraser Daly, Matthias Schulte, Seva Shneer
We consider first passage percolation on the Erdős--Rényi graph with vertices in which each pair of distinct vertices is connected independently by an edge with probability $λ/…
Moderate deviations on Poisson chaos
Matthias Schulte, Christoph Thaele
This paper deals with U-statistics of Poisson processes and multiple Wiener-Itô integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variabl…
Lower bounds for variances of Poisson functionals
Matthias Schulte, Vanessa Trapp
Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the differ…
Dickman Approximation of weighted random sums in the Kolmogorov distance
Chinmoy Bhattacharjee, Matthias Schulte
We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other area…
Normal approximation of Kabanov-Skorohod integrals on Poisson spaces
Günter Last, Ilya Molchanov, Matthias Schulte
We consider the normal approximation of Kabanov-Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only diffe…
Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes
Carina Betken, Matthias Schulte, Christoph Thäle
This paper deals with the union set of a stationary Poisson process of cylinders in having an -dimensional base and an -dimensional direction space, where…
Poisson process approximation under stabilization and Palm coupling
Omer Bobrowski, Matthias Schulte, D. Yogeshwaran
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range o…
Poisson approximation with applications to stochastic geometry
Federico Pianoforte, Matthias Schulte
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides,…
Rates of multivariate normal approximation for statistics in geometric probability
Matthias Schulte, J. E. Yukich
We employ stabilization methods and second order Poincaré inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})…
Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations
Federico Pianoforte, Matthias Schulte
This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a…
Non-standard limits for a family of autoregressive stochastic sequences
Sergey Foss, Matthias Schulte
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoreg…
Large degrees in scale-free inhomogeneous random graphs
Chinmoy Bhattacharjee, Matthias Schulte
We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observatio…
Testing multivariate uniformity based on random geometric graphs
Bruno Ebner, Franz Nestmann, Matthias Schulte
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set based on statistics related to edge lengths of random geometric graphs. Asym…
The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation
Günter Last, Franz Nestmann, Matthias Schulte
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson point…
Multivariate second order Poincaré inequalities for Poisson functionals
Matthias Schulte, J. E. Yukich
Given a vector of Poisson functionals , we investigate the proximity between and an -dimensional centered Gaussian random vector wit…
Normal approximation for stabilizing functionals
Raphaël Lachièze-Rey, Matthias Schulte, J. E. Yukich
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point…
Second order analysis of geometric functionals of Boolean models
Daniel Hug, Michael A. Klatt, Günter Last +1
This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translati…
Poisson point process convergence and extreme values in stochastic geometry
Matthias Schulte, Christoph Thaele
Let be a Poisson point process with intensity measure , , over a Borel space , where is a fixed measure. Another point process on the real line…
Central limit theorems for the radial spanning tree
Matthias Schulte, Christoph Thaele
Consider a homogeneous Poisson point process in a compact convex set in -dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree…
Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem
Matthias Schulte, Christoph Thaele
A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gauss…
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry
Laurent Decreusefond, Matthias Schulte, Christoph Thäle
A Poisson or a binomial process on an abstract state space and a symmetric function acting on -tuples of its points are considered. They induce a point process on the target…
Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
Günter Last, Giovanni Peccati, Matthias Schulte
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poiss…
Limit theory for the Gilbert graph
Matthias Reitzner, Matthias Schulte, Christoph Thaele
For a given homogeneous Poisson point process in two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour o…