Extreme value theory for constrained physical systems

Physical Review. E
Marc HöllEli Barkai

Abstract

We investigate extreme value theory for physical systems with a global conservation law which describes renewal processes, mass transport models, and long-range interacting spin models. As shown previously, a special feature is that the distribution of the extreme value exhibits a nonanalytical point in the middle of the support. We expose exact relationships between constrained extreme value theory and well-known quantities of the underlying stochastic dynamics, all valid beyond the midpoint in general, i.e., even far from the thermodynamic limit. For example, for renewal processes the distribution of the maximum time between two renewal events is exactly related to the mean number of these events. In the thermodynamic limit, we show how our theory is suitable to describe typical and rare events which deviate from classical extreme value theory. For example, for the renewal process we unravel dual scaling of the extreme value distribution, pointing out two types of limiting laws: a normalizable scaling function for the typical statistics and a non-normalized state describing the rare events.

References

Feb 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S B Lowen, M C Teich
Mar 24, 2005·Physical Review Letters·G Margolin, E Barkai
May 21, 2005·Physical Review Letters·Satya N MajumdarR K P Zia
Aug 8, 2009·Physical Review Letters·Claude GodrècheGrégory Schehr
Sep 28, 2010·Physical Review Letters·David A Kessler, Eli Barkai
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takuma Akimoto, Tomoshige Miyaguchi
Feb 4, 2014·Physical Review Letters·Amir Bar, David Mukamel
Apr 8, 2014·Physical Review Letters·Adi RebenshtokEli Barkai
May 30, 2015·Physical Review Letters·Baruch Meerson, S Redner
Jun 15, 2016·Physical Review. E·Amir BarDavid Mukamel
May 3, 2019·The Journal of Chemical Physics·Xudong WangYao Chen
Sep 11, 2019·Physical Review. E·Alessandro VezzaniRaffaella Burioni
Feb 19, 2020·Scientific Reports·Alessandro VezzaniRaffaella Burioni
Jun 25, 2020·Physical Review. E·Takuma AkimotoGünter Radons

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Citations

Dec 18, 2020·Physical Review. E·Wanli WangEli Barkai
Jun 18, 2021·Physical Review. E·Prashant Singh, Arnab Pal

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