scholarly journals Conformal covariance of the Abelian sandpile height one field

2009 ◽  
Vol 119 (9) ◽  
pp. 2725-2743 ◽  
Author(s):  
Maximilian Dürre
Keyword(s):  
Abelian Sandpile ◽  
Conformal Covariance

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

Conformal covariance of field equations

1970 ◽  
Vol 61 (1) ◽  
pp. 78-97 ◽  
Author(s):  
Moshe Flato ◽  
Jacques Simon ◽  
Daniel Sternheimer
Keyword(s):  
Field Equations ◽  
Conformal Covariance

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

MOYAL STAR PRODUCT OF μ-HOLOMORPHIC j-DIFFERENTIALS

2008 ◽  
Vol 05 (03) ◽  
pp. 363-373
Author(s):  
M. KACHKACHI
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Quantum Effect ◽  
Star Product ◽  
Complex Structure ◽  
Complex Structures ◽  
Star Products ◽  
First Order ◽  
Conformal Fields ◽  
Conformal Covariance

It was shown in [1], only for scalar conformal fields, that the Moyal–Weyl star product can introduce the quantum effect as the phase factor to the ordinary product. In this paper we show that, even on the same complex structure, the Moyal–Weyl star product of two j-differentials (conformal fields of weights (j, 0)) does not vanish but it generates the quantum effect at the first order of its perturbative series. More generally, we get the explicit expression of the Moyal–Weyl star product of j-differentials defined on any complex structure of a bi-dimensional Riemann surface Σ. We show that the star product of two j-differentials is not a j-differential and does not preserve the conformal covariance character. This can shed some light on the Moyal–Weyl deformation quantization procedure connection's with the deformation of complex structures on a Riemann surface. Hence, the situation might relate the star products to the Moduli and Teichmüller spaces of Riemann surfaces.

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
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