7 papers
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 Martín 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 sensitiv…
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 Volume of Random Projections and Sections of -balls
Joscha Prochno, Christoph Thaele, Philipp Tuchel
Let be the -dimensional unit ball corresponding to the -norm. For each we sample a uniform random subspace of fixed dimension $m\i…
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…