Universal to nonuniversal transition of the statistics of rare events during the spread of random walks

R. K. Singh, Stanislav Burov

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 languageEnglish
Article numberL052102
Number of pages6
JournalPhysical Review E
Volume108
Issue number5
DOIs
StatePublished - 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.

FundersFunder number
Israel Academy of Sciences and Humanities
Israel Science Foundation2796/20
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