scholarly journals Convergence of the random Abelian sandpile

2021 ◽  
Vol 49 (6) ◽  
Author(s):  
Ahmed Bou-Rabee
Keyword(s):  
Abelian Sandpile

scholarly journals On the sandpile model of modified wheels II

2020 ◽  
Vol 18 (1) ◽  
pp. 1531-1539
Author(s):  
Zahid Raza ◽  
Mohammed M. M. Jaradat ◽  
Mohammed S. Bataineh ◽  
Faiz Ullah
Keyword(s):  
Direct Product ◽  
Critical Group ◽  
Complete Structure ◽  
Sandpile Model ◽  
Cyclic Subgroups ◽  
Algebr Comb ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
Sandpile Group

Abstract We investigate the abelian sandpile group on modified wheels {\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on {\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on {\hat{W}}_{n} is the direct product of two cyclic subgroups of order {a}_{n} and 3{a}_{n} for n even and of order {a}_{n} and 2{a}_{n} for n odd, respectively.

scholarly journals Multiple and inverse topplings in the Abelian Sandpile Model

2012 ◽  
Vol 212 (1) ◽  
pp. 23-44 ◽  
Author(s):  
S. Caracciolo ◽  
G. Paoletti ◽  
A. Sportiello
Keyword(s):  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
Abelian Sandpile

scholarly journals Mixing time and eigenvalues of the abelian sandpile Markov chain

2019 ◽  
Vol 372 (12) ◽  
pp. 8307-8345
Author(s):  
Daniel C. Jerison ◽  
Lionel Levine ◽  
John Pike
Keyword(s):  
Markov Chain ◽  
Mixing Time ◽  
Abelian Sandpile

Critical exponents for boundary avalanches in two-dimensional Abelian sandpile

1994 ◽  
Vol 27 (16) ◽  
pp. L585-L590 ◽  
Author(s):  
E V Ivashkevich ◽  
D V Ktitarev ◽  
V B Priezzhev
Keyword(s):  
Critical Exponents ◽  
Two Dimensional ◽  
Abelian Sandpile

scholarly journals Avalanches and waves in the Abelian sandpile model

1997 ◽  
Vol 56 (4) ◽  
pp. R3745-R3748 ◽  
Author(s):  
Maya Paczuski ◽  
Stefan Boettcher
Keyword(s):  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
Abelian Sandpile

Waves of topplings in an Abelian sandpile

1994 ◽  
Vol 209 (3-4) ◽  
pp. 347-360 ◽  
Author(s):  
E.V. Ivashkevich ◽  
D.V. Ktitarev ◽  
V.B. Priezzhev
Keyword(s):  
Abelian Sandpile
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