2024/12/08 by Alon Agin, Agin, Alon, Barak Weiss +1
Computer Science · #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2412.05858
Akhunzhanov and Shatskov defined the Dirichlet spectrum, corresponding to m × n matrices and to norms on ℝm and ℝn. In case (m,n) = (2,1) and using the Euclidean norm on ℝ2, they showed that the spectrum is an interval. We generalize this result to arbitrary (m,n) ≠ (1,1) and arbitrary norms, improving previous works from recent years. We also define some related spectra and show that they too are intervals. Our argument is a modification of an argument of Khintchine from 1926.