Sandpiles on the Square Lattice View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Robert D. Hough, Daniel C. Jerison, Lionel Levine

ABSTRACT

We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice Z2 . We also determine the asymptotic spectral gap, asymptotic mixing time, and prove a cutoff phenomenon for the recurrent state abelian sandpile model on the torus Z/mZ2 . The techniques use analysis of the space of functions on Z2 which are harmonic modulo 1. In the course of our arguments, we characterize the harmonic modulo 1 functions in ℓp(Z2) as linear combinations of certain discrete derivatives of Green’s functions, extending a result of Schmidt and Verbitskiy (Commun Math Phys 292(3):721–759, 2009. arXiv:0901.3124 [math.DS]). More... »

PAGES

33-87

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-019-03408-5

DOI

http://dx.doi.org/10.1007/s00220-019-03408-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112829535


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