On the Probability Distribution of Relaxation Length in a Parametric One-Dimensional Tropical Sandpile Model

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.