Aging arcsine law in Brownian motion and its generalization
| Autor: | Toru Sera, Kouji Yano, Takuma Akimoto, Kosuke Yamato |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistical Mechanics (cond-mat.stat-mech)
Generalization Probability (math.PR) FOS: Physical sciences Nonlinear Sciences - Chaotic Dynamics 01 natural sciences 010305 fluids & plasmas Distribution (mathematics) Mathematics::Probability Law 0103 physical sciences FOS: Mathematics Arcsine distribution Inverse trigonometric functions Fraction (mathematics) Limit (mathematics) Chaotic Dynamics (nlin.CD) 010306 general physics Constant (mathematics) Brownian motion Mathematics - Probability Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes. 7 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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