POISSON APPROXIMATION AND WEIBULL ASYMPTOTICS IN THE GEOMETRY OF NUMBERS
Artikel i vetenskaplig tidskrift, 2022

Minkowski's First Theorem and Dirichlet's Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study the distribution of such minima and show, under some technical conditions, that they exhibit Weibull asymptotics with respect to different natural measures on the space of unimodular lattices in Rd. This follows from very general Poisson approximation results for shrinking targets which should be of independent interest. Furthermore, we show in the appendix that the logarithm laws of Kleinbock-Margulis [Invent. Math. 138 (1999), pp. 451-494], Khinchin and Gallagher [J. London Math. Soc. 37 (1962), pp. 387-390] can be deduced from our distributional results.

Quantitative equidistribution

Key words and phrases

Poisson approxima-tion

multiple mixing

Weibull asymptotics

Författare

Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Alexander Gorodnik

Universität Zürich

Transactions of the American Mathematical Society

0002-9947 (ISSN) 1088-6850 (eISSN)

Vol. In Press

Ämneskategorier

Geometri

Diskret matematik

Matematisk analys

DOI

10.1090/tran/8826

Mer information

Senast uppdaterat

2023-10-27