Abstract
We study the statistics of increments in record values in a time series generated by the positions of a random walk (discrete time, continuous space) of duration steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of for large , and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability that the record increments decrease monotonically up to step . Remarkably, is universal (i.e., independent of the jump distribution) for each , decaying as for large , with a universal amplitude .
- Received 5 April 2016
DOI:https://doi.org/10.1103/PhysRevLett.117.010601
© 2016 American Physical Society