Time Between the Maximum and the Minimum of a Stochastic Process.
Phys Rev Lett
; 123(20): 200201, 2019 Nov 15.
Article
em En
| MEDLINE
| ID: mdl-31809107
ABSTRACT
We present an exact solution for the probability density function P(τ=t_{min}-t_{max}|T) of the time difference between the minimum and the maximum of a one-dimensional Brownian motion of duration T. We then generalize our results to a Brownian bridge, i.e., a periodic Brownian motion of period T. We demonstrate that these results can be directly applied to study the position difference between the minimal and the maximal heights of a fluctuating (1+1)-dimensional Kardar-Parisi-Zhang interface on a substrate of size L, in its stationary state. We show that the Brownian motion result is universal and, asymptotically, holds for any discrete-time random walk with a finite jump variance. We also compute this distribution numerically for Lévy flights and find that it differs from the Brownian motion result.
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1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev Lett
Ano de publicação:
2019
Tipo de documento:
Article
País de afiliação:
França