Statistical theory of hierarchical avalanche ensemble
Alexander I. Olemskoi (Sumy State University)
TL;DR
This paper develops a statistical framework for analyzing avalanche ensembles in ultrametric spaces, deriving key distributions, currents, and critical conditions for global avalanche formation.
Contribution
It introduces a novel statistical approach to hierarchical avalanches, providing analytical expressions for intensity distributions and critical thresholds.
Findings
Derived stationary intensity distribution and steady-state current.
Calculated critical avalanche intensity as a function of noise.
Obtained large-time asymptotics for global avalanche probability.
Abstract
The statistical ensemble of avalanche intensities is considered to investigate diffusion in ultrametric space of hierarchically subordinated avalanches. The stationary intensity distribution and the steady-state current are obtained. The critical avalanche intensity needed to initiate the global avalanche formation is calculated depending on noise intensity. The large time asymptotic for the probability of the global avalanche appearance is derived.
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Taxonomy
Topicsadvanced mathematical theories