Extreme Event Statistics in a Drifting Markov Chain
arXiv:1702.07582 · doi:10.1103/PhysRevE.96.012130
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.
9 pages, 10 figures
References in corpus (9)
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Universal Record Statistics of Random Walks and Lévy Flights
- Record statistics and persistence for a random walk with a drift
- Records in a changing world
- Nonergodic Diffusion of Single Atoms in a Periodic Potential
- Scaling in Tournaments
- Record Statistics of Continuous Time Random Walk
- Record statistics of financial time series and geometric random walks
- On the effect of random inhomogeneities in Kerr-media modelled by non-linear Schrodinger equation