Joscha Prochno

activity

20232026

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math.PR2025

Limit theorems for the distance between two 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 their boundaries accor…

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…

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