Abstract:Sums of independent exponential random variables lead to the Erlang distribution, providing a direct probabilistic route from exponential waiting times to the integer-shape gamma law. This paper investigates how this classical construction changes when the exponential waiting-time density is replaced by the $q$-exponential density of nonextensive statistics. Our main result is an analytical asymptotic expression for the outflow of a mass-conserving cascade of reservoirs driven by a $q$-exponential waiting-time kernel. In the critical case $q=5/3$, the large-cascade flow rate converges to a stable Lévy density whose time argument is shifted by a Galilean-type transformation. This shifted Lévy law gives the asymptotic hydrograph of the cascade. We also found that for the entire regime $1<q<2$ the macroscopic dynamics are governed by $\alpha$-stable Lévy laws. This proves that anomalous non-Gaussian dispersion can emerge from pure mass-conserving convolutional chains without invoking fractional derivatives.
From: Henrique Lima [view email]
[v1]
Fri, 19 Jun 2026 04:52:02 UTC (456 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。