Joscha Prochno

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20242026

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math.PR2026

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--PoincarÃ©--Borel laws for their curvature measures

Zakhar Kabluchko, Alexander Marynych, Joscha Prochno

For $p > 1$ , we derive explicit formulas for the intrinsic volumes $V_{0} (B_{p}^{n}), \dots, V_{n - 1} (B_{p}^{n})$ of the $n$ -dimensional $ℓ_{p}$ -balls $$ \mathbb B_p^n = \{x\in\m…

math.PR2026

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 $I^½$ and self-similarity index $I^\pm > 0$ . Let $e^{- m_{t}}$ denote the size of the largest fragment at time $t \ge…

math.PR2026

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…

math.PR2025

Limit theorems for the distance of random points in $l_{p}^{n}$ -balls

David Alonso-GutiÃ©rrez, Javier MartÃn GoÃ±i, Joscha Prochno

In this paper, we prove that the Euclidean distance between two independent random vectors uniformly distributed on $l_{p}^{n}$ -balls $(1 \leq p \leq \infty)$ or on its boundary satisf…

math.PR2024

Limit Theorems for the Volume of Random Projections and Sections of $ℓ_{p}^{N}$ -balls

Joscha Prochno, Christoph Thaele, Philipp Tuchel

Let $B_{p}^{N}$ be the $N$ -dimensional unit ball corresponding to the $ℓ_{p}$ -norm. For each $N \in N$ we sample a uniform random subspace $E_{N}$ of fixed dimension $m\i…

math.PR2024

The macroscopic shape of Gelfand-Tsetlin patterns and free probability

Samuel G. G. Johnston, Joscha Prochno

A compression is a function $F : R \times [0, 1] \to [0, 1]$ such that each $F (\cdot, I ¨ )$ is the distribution function of a measure of mass $I ¨ $ , while each $F (x, \cdot)$ is increa…

Intrinsic volumes of ℓp​-balls and a continuum of Maxwell--PoincarÃ©--Borel laws for their curvature measures

The largest fragment in self-similar fragmentation processes of positive index

Large deviations for sums of multivariate stretched-exponential random variables: the few-big-jumps principle

Limit theorems for the distance of random points in lpn​-balls

Limit Theorems for the Volume of Random Projections and Sections of ℓpN​-balls

The macroscopic shape of Gelfand-Tsetlin patterns and free probability

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--PoincarÃ©--Borel laws for their curvature measures

Limit theorems for the distance of random points in $l_{p}^{n}$ -balls

Limit Theorems for the Volume of Random Projections and Sections of $ℓ_{p}^{N}$ -balls