TY - JOUR

T1 - Extreme value theory for constrained physical systems

AU - Höll, Marc

AU - Wang, Wanli

AU - Barkai, Eli

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/10/29

Y1 - 2020/10/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85095584682&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.102.042141

DO - 10.1103/PhysRevE.102.042141

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C2 - 33212632

AN - SCOPUS:85095584682

SN - 2470-0045

VL - 102

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 042141

ER -