TY - JOUR

T1 - Universal to nonuniversal transition of the statistics of rare events during the spread of random walks

AU - Singh, R. K.

AU - Burov, Stanislav

N1 - Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/11

Y1 - 2023/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85176617020&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.108.L052102

DO - 10.1103/PhysRevE.108.L052102

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AN - SCOPUS:85176617020

SN - 2470-0045

VL - 108

JO - Physical Review E

JF - Physical Review E

IS - 5

M1 - L052102

ER -