Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks

Details Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks

2009-10-26

arxiv.org/abs/0910.4913v1

J. Stat. Mech. P01009 (2010)

Physics

Condensed Matter

Statistical Mechanics

24 pages, 5 figures

Scientific paper

10.1088/1742-5468/2010/01/P01009

We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, and extending others. We apply the same method to compute the distribution of extrema of Bessel processes. We briefly show how the continuous time random walk (CTRW) corresponds to a non standard fixed point of the RSRG transformation.

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