Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton
Abstract
Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2010
- DOI:
- 10.48550/arXiv.1009.4609
- arXiv:
- arXiv:1009.4609
- Bibcode:
- 2010arXiv1009.4609B
- Keywords:
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- Nonlinear Sciences - Cellular Automata and Lattice Gases;
- Condensed Matter - Statistical Mechanics;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Physics - Geophysics
- E-Print:
- improved, new material added