Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2015/07/P07026
Keywords
fluctuations (theory); stochastic processes (theory); extreme value statistics
Categories
Funding
- Indo-French Centre for the Promotion of Advanced Research [4604-3]
Ask authors/readers for more resources
We investigate the statistics of records in a random sequence {x(B)(0) = 0, x(B)(1), ... , x(B)(n) = x(B)(0) = 0} of n time steps. The sequence x(B)(k)'s represents the position at step k of a random walk 'bridge' of n steps that starts and ends at the origin. At each step, the increment of the position is a random jump drawn from a specified symmetric distribution. We study the statistics of records and record ages for such a bridge sequence, for different jump distributions. In absence of the bridge condition, i.e. for a free random walk sequence, the statistics of the number and ages of records exhibits a 'strong' universality for all n, i.e. they are completely independent of the jump distribution as long as the distribution is continuous. We show that the presence of the bridge constraint destroys this strong 'all n' universality. Nevertheless a 'weaker' universality still remains for large n, where we show that the record statistics depends on the jump distributions only through a single parameter 0 < mu <= 2, known as the Levy index of the walk, but are insensitive to the other details of the jump distribution. We derive the most general results (for arbitrary jump distributions) wherever possible and also present two exactly solvable cases. We present numerical simulations that verify our analytical results.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available