5 research outputs found
Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks
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.Comment: 24 pages, 5 figure