Alireza Salehi Golsefidi UCSD
Random walk in compact groups

Two new concepts related to random walks on compact groups will be presented: local randomness and spectral independence of two compact groups. Basic properties of locally random groups and important examples of such groups will be mentioned. In order to motivate the definition of spectral independence, super-approximation conjecture will be formulated; this conjecture roughly says the behavior of random walk in the closure of certain linear groups is dictated by their Zariski-closure. At the end it will be mentioned that open compact subgroups of two non-isomorphic simple analytic groups are spectrally independent. (This is a joint work with K. Mallahi Karai and A. Mohammadi)