학술논문
Sandpile transience on the grid is polynomially bounded
Document Type
Conference
Author
Source
Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms. :627-636
Subject
Language
English
Abstract
We study the process of adding one grain at a time in the Abelian Sandpile Model (ASM) based on the n X n grid (Bak et al., 1988, Dhar, 1990, Dhar et al., 1995). We prove that within a polynomial (in n) number of steps, we necessarily reach a recurrent configuration regardless of the choice of sites where the grains are dropped. This adds credence to the common notion that "recurrence" represents "longterm behavior" of the system.