Abstract
In this work, we introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of small balls, and provide several examples of such groups. In particular, this leads to new examples of groups satisfying such a mixing inequality. In the same context, we develop a Littlewood–Paley decomposition and explore its connection to the existence of a spectral gap for random walks. Moreover, under the dimension condition alone, we prove a multi-scale entropy gain result à la Bourgain–Gamburd and Tao.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
