Analysis reveals probability distribution of relaxation length in tropical sandpile models, suggesting new insights into stationary points.
A special case of the one-dimensional tropical sandpile model is introduced, incorporating a parameter that affects the deformation of the hypersurface. We focus on study of relaxation behaviour towards finite stationary points. Particularly, for two stationary points randomly taken from $$[0,1]$$ we derived probability distribution function of relaxation length. Numerical experiments for uniformly distributed stationary points are given and coincide with the theoretical inferences.
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Alexander Varypaev (2025) studied this question.
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