5 papers
Limit laws for longest edges in empty region graphs
Holger Sambale, Matthias Schulte, Christoph Thaele
Empty region graphs are graphs whose vertices are points in and where two vertices are connected by an edge whenever some associated region does not contain any othe…
Some notes on higher order concentration of measure
Holger Sambale
This survey-type paper provides a common framework for a larger number of higher order concentration results (i.\,e., concentration results for non-Lipschitz functions which have b…
Central limit theorems for the nearest neighbour embracing graph in Euclidean and hyperbolic space
Holger Sambale, Christoph Thäle, Tara Trauthwein
Consider a stationary Poisson process in the -dimensional Euclidean or hyperbolic space and construct a random graph with vertex set as follows. First, each point $x\i…
Some notes on moment inequalities for heavy-tailed distributions
Paul Buterus, Holger Sambale
We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of exampl…
Concentration of measure on spheres and related manifolds
Friedrich Götze, Holger Sambale
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration resul…