Extreme values and logarithm laws for toral translations
Sourav Das, Anish Ghosh, Sundara Narasimhan
Abstract
We study extreme values of normalized r-th nearest neighbour distance functions in inhomogeneous Diophantine approximation, proving Weibull and Fréchet limit laws when the shift satisfies a natural Diophantine condition. Using these extreme value laws we prove corresponding logarithm laws for these functions. Our approach is based on homogeneous dynamics. The key input is to adapt the Poisson approximation strategy of Björklund and Gorodnik (arXiv:2201.05116) combined with an effective multiple equidistribution result, which we deduce using results of Strömbergsson (arXiv:1309.6103) and of Björklund and Gorodnik (arXiv:2105.05468).
Create a lesson
Related papers
Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups
Liming Ma, Yipeng Wang
Tunnell-type criteria for variants of the congruent number problem
Bo-Hae Im, Minseo Shin
A uniform effective André--Oort result
Guy Fowler
On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients
Ken Ono, Ashvin Swaminathan
On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
Chieh-Yu Chang, Song-Yun Chen, Fei-Jun Huang et al.
Stable Trace Formula for Newton strata of Shimura varieties
Dhruva Kelkar