Abstract:
The phenomenon of probability gaps suggests that if a property holds in a finite group with high probability, it often holds universally within the group. Extending this idea to infinite group is challenging, in the absence of a natural probability measure. In the talk I’ll discuss probability gaps on infinite groups measured by random walks, and present recent results, joint with Greenfeld and Olshanskii, answering a few questions of Amir, Blachar, Gerasimova, and Kozma.
