A Generalized Lévy-Khintchine Theorem
Ergodic Theory and Dynamical Systems Seminar
20th March 2025, 2:00 pm – 3:00 pm
Fry Building, 2.04
The classical Lévy-Khintchine theorem describes the limiting distribution of the denominators of continued fraction convergents of a real number. In a recent breakthrough, Cheung and Chevallier extended this theorem to higher dimensions by considering best approximates of matrices. In this talk, I will present results that further generalize their work by introducing multiple natural notions of best approximates for matrices and proving Lévy-Khintchine-type theorems in all these settings.
Our results not only answer a question posed by Cheung and Chevallier about Lévy-Khintchine-type theorems for arbitrary norms but also resolve a conjecture of Yitwah Cheung. Additionally, we extend the results of Cheung and Chevallier by proving their theorems for almost every point with respect to a broad class of measures, including fractal measures, while allowing best approximates to satisfy additional geometric and arithmetic constraints. This work also extends recent results of Shapira and Weiss.
The talk is based on joint work with Anish Ghosh, see https://arxiv.org/pdf/2408.15683.
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