Speaker: Gaurav Aggarwal
Affiliation: TIFR
Title: L\'{e}vy-Khintchine Theorems: effective results and central limit theorems
Date and Time: April 30, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: The L´evy-Khintchine theorem is a famous result in Diophantine approxima- tion describing the growth rate of denominators of convergents in the continued fraction expansion of a typical number. We make the theorem effective by providing a rate of con- vergence. Recently, Cheung and Chevallier (Annales scientifiques de l’ENS, 2024) proved a higher dimensional, simultaneous approximation analogue of the L´e vy-Khintchine theorem. Their work provides a limiting law for the denominators of best approximations. We also make their theorem effective by providing a rate for the convergence. Moreover, we prove a central limit theorem in this context. Our methods are completely different and are drawn from homogeneous dynamics.
Affiliation: TIFR
Title: L\'{e}vy-Khintchine Theorems: effective results and central limit theorems
Date and Time: April 30, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: The L´evy-Khintchine theorem is a famous result in Diophantine approxima- tion describing the growth rate of denominators of convergents in the continued fraction expansion of a typical number. We make the theorem effective by providing a rate of con- vergence. Recently, Cheung and Chevallier (Annales scientifiques de l’ENS, 2024) proved a higher dimensional, simultaneous approximation analogue of the L´e vy-Khintchine theorem. Their work provides a limiting law for the denominators of best approximations. We also make their theorem effective by providing a rate for the convergence. Moreover, we prove a central limit theorem in this context. Our methods are completely different and are drawn from homogeneous dynamics.