Back to Search
Start Over
Poisson approximation and Weibull asymptotics in the geometry of numbers.
- Source :
- Transactions of the American Mathematical Society; Mar2023, Vol. 376 Issue 3, p2155-2180, 26p
- Publication Year :
- 2023
-
Abstract
- 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 \mathbb {R}^d. 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- EUCLIDEAN domains
GEOMETRY
MATHEMATICS
LOGARITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 376
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 161933414
- Full Text :
- https://doi.org/10.1090/tran/8826