Record statistics for random walks and L\'evy flights with resetting
| العنوان: | Record statistics for random walks and L\'evy flights with resetting |
|---|---|
| المؤلفون: | Satya N Majumdar, Philippe Mounaix, Sanjib Sabhapandit, Grégory Schehr |
| المساهمون: | Le Vaou, Claudine |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Statistics and Probability, Mathematics::Functional Analysis, Modeling and Simulation, High Energy Physics::Phenomenology, General Physics and Astronomy, Statistical and Nonlinear Physics, Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Probability, [PHYS] Physics [physics] |
| الوصف: | We compute exactly the mean number of records $\langle R_N \rangle$ for a time-series of size $N$ whose entries represent the positions of a discrete time random walker on the line. At each time step, the walker jumps by a length $\eta$ drawn independently from a symmetric and continuous distribution $f(\eta)$ with probability $1-r$ (with $0\leq r < 1$) and with the complementary probability $r$ it resets to its starting point $x=0$. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for $r=0$) and an uncorrelated time-series (for $(1-r) \ll 1$). Remarkably, we found that for every fixed $r \in [0,1[$ and any $N$, the mean number of records $\langle R_N \rangle$ is completely universal, i.e., independent of the jump distribution $f(\eta)$. In particular, for large $N$, we show that $\langle R_N \rangle$ grows very slowly with increasing $N$ as $\langle R_N \rangle \approx (1/\sqrt{r})\, \ln N$ for $0 Comment: 24 pages, 7 figures. Version submitted for publication |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aef9e2ab15801093cf06bb17a65ba4d2 http://arxiv.org/abs/2110.01539 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....aef9e2ab15801093cf06bb17a65ba4d2 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |