Details

Autor(en) / Beteiligte

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

Titel

Sandpiles on the Square Lattice

Ist Teil von

• Communications in mathematical physics, 2019-04, Vol.367 (1), p.33-87

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2019

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice Z 2 . 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 / m Z 2 . The techniques use analysis of the space of functions on Z 2 which are harmonic modulo 1. In the course of our arguments, we characterize the harmonic modulo 1 functions in ℓ p ( Z 2 ) 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]).