37 citations · 137 across the 20 of their papers we have counts for
20 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\inη…
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…
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…
Higher order concentration on Stiefel and Grassmann manifolds
Friedrich Götze, Holger Sambale
We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functio…
Probabilistic Limit Theorems Induced by the Zeros of Polynomials
Nils Heerten, Holger Sambale, Christoph Thäle
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds…
Large deviations for uniform projections of -radial distributions on -balls
Tom Kaufmann, Holger Sambale, Christoph Thäle
We consider products of uniform random variables from the Stiefel manifold of orthonormal -frames in , , and random vectors from the -dimensional $\ell…
Fluctuations of the magnetization in the Block Potts Model
Jonas Jalowy, Matthias Löwe, Holger Sambale
In this note we study the block spin mean-field Potts model, in which the spins are divided into blocks and can take different values (colors). Each block is allowed t…
Concentration inequalities on the multislice and for sampling without replacement
Holger Sambale, Arthur Sinulis
We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomial…
Large deviations and a phase transition in the Block Spin Potts models
Holger Knöpfel, Matthias Löwe, Holger Sambale
We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in…
Concentration on Poisson spaces via modified -Sobolev inequalities
Anna Gusakova, Holger Sambale, Christoph Thaele
Concentration properties of functionals of general Poisson processes are studied. Using a modified -Sobolev inequality a recursion scheme for moments is established, which is of…
Some notes on concentration for -subexponential random variables
Holger Sambale
We prove extensions of classical concentration inequalities for random variables which have -subexponential tail decay for any . This includes Hanson--Wright type an…
Modified log-Sobolev inequalities and two-level concentration
Holger Sambale, Arthur Sinulis
We consider a generic modified logarithmic Sobolev inequality (mLSI) of the form for some difference operator , and s…
Concentration inequalities for polynomials in -sub-exponential random variables
Friedrich Götze, Holger Sambale, Arthur Sinulis
In this work we derive multi-level concentration inequalities for polynomial functions in independent random variables with a -sub-exponential tail decay. A particularly interes…
Concentration inequalities for bounded functionals via generalized log-Sobolev inequalities
Friedrich Götze, Holger Sambale, Arthur Sinulis
In this paper we prove multilevel concentration inequalities for bounded functionals of random variables that are either independent or…
Logarithmic Sobolev inequalities for finite spin systems and applications
Holger Sambale, Arthur Sinulis
We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these condi…
Higher order concentration in presence of Poincaré-type inequalities
Friedrich Götze, Holger Sambale
We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order for any . Here we focus on different…
Higher order concentration for functions of weakly dependent random variables
Friedrich Götze, Holger Sambale, Arthur Sinulis
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies…
Higher Order Concentration of Measure
Sergey G. Bobkov, Friedrich Götze, Holger Sambale
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order for any . The bounds are based on $…