Emergence of power law distributions for odd and even lifetimes

SILVIA MENCHÓN; PABLO MANUEL ROMÁN

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2020

1539-3755

Avalanche lifetime distributions have been related to first-return random walk processes. In this sense the theory for random walks can be employed to understand, for instance, the origin of power law distributions in self-organized criticality. In this work we study first return probability distributions, f^(n), for discrete random walks with constant one step transition probabilities. Explicit expressions are given in terms of 2F1 hypergeometric functions, allowing us to study the different behaviors of f^(n) for odd and even values of n. We show that the first return probabilities have a power law behavior with exponent -3/2 only when the random walk is unbiased. In any other case, it presents an exponential decay.