7 papers
Intrinsic volumes of -balls and a continuum of Maxwell--Poincaré--Borel laws for their curvature measures
Zakhar Kabluchko, Alexander Marynych, Joscha Prochno
For , we derive explicit formulas for the intrinsic volumes of the -dimensional -balls $$ \mathbb B_p^n = \{x\in\m…
The largest fragment in self-similar fragmentation processes of positive index
Piotr Dyszewski, Samuel G. G. Johnston, Sandra Palau +1
We study a self-similar fragmentation process with dislocation measure and self-similarity index . Let denote the size of the largest fragment at time $t \ge…
Large deviations for sums of multivariate stretched-exponential random variables: the few-big-jumps principle
Nina Gantert, Joscha Prochno, Philipp Tuchel
Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, goi…
Limit theorems for the distance of random points in -balls
David Alonso-Gutiérrez, Javier MartÃn Goñi, Joscha Prochno
In this paper, we prove that the Euclidean distance between two independent random vectors uniformly distributed on -balls or on its boundary satisf…
Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits
Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno
We study the asymptotic behavior of cumulants of lacunary trigonometric sums , , and show that cumulant growth is highly sens…
A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums
Christoph Aistleitner, Lorenz Fruehwirth, Joscha Prochno
A classical observation in analysis asserts that lacunary systems of dilated functions show many properties which are also typical for systems of independent random variables. For…