Abstract
Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e-|x|β (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.
Original language | English |
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Article number | L052102 |
Number of pages | 6 |
Journal | Physical Review E |
Volume | 108 |
Issue number | 5 |
DOIs | |
State | Published - Nov 2023 |
Bibliographical note
Publisher Copyright:© 2023 American Physical Society.
Funding
This work was supported by the Israel Science Foundation Grant No. 2796/20. R.K.S. thanks the Israel Academy of Sciences and Humanities (IASH) and the Council of Higher Education (CHE) Fellowship.
Funders | Funder number |
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Israel Academy of Sciences and Humanities | |
Israel Science Foundation | 2796/20 |
Yükseköğretim Kurulu |