Joscha Prochno

activity

20232026

collaborators

10 papers

math.PR2026

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--Poincaré--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

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-Gutiérrez, Javier Martín Goñi, 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.NT2025

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 $S_{n} (ω) := \sum_{k = 1}^{n} cos (2 π a_{k} ω)$ , $ω \in [0, 1]$ , and show that cumulant growth is highly sensitiv…

math.NT2025

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…

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.HO2024

Talagrand's mathematical journey to the Abel Prize 2024

Olivier Guédon, Joscha Prochno

Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis…

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 $F (\cdot, τ)$ is the distribution function of a measure of mass $τ$ , while each $F (x, \cdot)$ is increasi…

math.PR2024

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 $ν$ and self-similarity index $α > 0$ . Let $e^{- m_{t}}$ denote the size of the largest fragment at time $t \geq…

math.CO2023

Random planar trees and the Jacobian conjecture

Elia Bisi, Piotr Dyszewski, Nina Gantert +3

We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F : C^{n} \to C^{n}$ who…

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

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

Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits

A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums

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

Talagrand's mathematical journey to the Abel Prize 2024

The macroscopic shape of Gelfand-Tsetlin patterns and free probability

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

Random planar trees and the Jacobian conjecture

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--Poincaré--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