Rhiannon Dougall

From the thermodynamic formalism to convolution of probability in discrete groups

This talk will involve analysis on a discrete countable group. The analysis we are interested in is to describe limiting quantities associated to self-convolution of a probability function. (Quantities associated to a random walks on the group.) This is well-studied in the case where the probability is symmetric (whence one also benefits from self-adjointness of related operators). I’ll motivate the topic with how fundamental quantities associated to the group often appear in the limit. I’ll also explain a new result: a ratio limit theorem for amenable groups, and highlight the role (and novelty) of a thermodynamic mindset in this area.