Title: Extreme Event Statistics in a Drifting Markov Chain,
Abstract: We analyse extreme event statistics of experimentally realized Markov chains
with various drifts. Our Markov chains are individual trajectories of a single
atom diffusing in a one dimensional periodic potential. Based on more than 500
individual atomic traces we verify the applicability of the Sparre Andersen
theorem to our system despite the presence of a drift. We present detailed
analysis of four different rare event statistics for our system: the
distributions of extreme values, of record values, of extreme value occurrence
in the chain, and of the number of records in the chain. We observe that for
our data the shape of the extreme event distributions is dominated by the
underlying exponential distance distribution extracted from the atomic traces.
Furthermore, we find that even small drifts influence the statistics of extreme
events and record values, which is supported by numerical simulations, and we
identify cases in which the drift can be determined without information about
the underlying random variable distributions. Our results facilitate the use of
extreme event statistics as a signal for small drifts in correlated
trajectories.