Motzkin numbers out of Random Domino Automaton |
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| Authors: | Mariusz Białecki |
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| Affiliation: | Institute of Geophysics, Polish Academy of Sciences, ul. Ks. Janusza 64, 01-452 Warszawa, Poland |
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| Abstract: | Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton. |
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| Keywords: | Avalanches Stochastic cellular automata Motzkin numbers Solvable models Exact solutions Toy models of earthquakes |
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