Ages of records in random walks

Abstract

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,... and for the probability that the record of the kth longest age is broken at step n. Furthermore, we show that the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

15 pages, 1 figure

References in corpus (3)

• Universal Record Statistics of Random Walks and Lévy Flights
• Universal statistics of longest lasting records of random walks and Lévy flights
• Statistics of the longest interval in renewal processes

Cited by in corpus (4)

• Record statistics of a strongly correlated time series: random walks and Lévy flights
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Longest interval between zeros of the tied-down random walk, the Brownian bridge and related renewal processes
• Two-time correlation and occupation time for the Brownian bridge and tied-down renewal processes