The Abelian sandpile model on an infinite tree

Annals of Probability

Volumn 30, Issue 4, 2002, Pages 2081-2107

  Maes, Christian ^a   Redig, Frank ^b   Saada, Ellen ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITÉ DE ROUEN   (France)

Author keywords

Interacting particle systems; Nonlocal interactions; Sandpile dynamics; Thermodynamic limit

Indexed keywords

EID: 0036821635     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1039548382     Document Type: Article

References (15)

1. BAK, P., TANG, K. and WIESENFELD, K. (1988). Self-organized criticality. Phys. Rev. A 38 364-374.
2. CHEN, M. F. (1992). From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, Singapore.
3. CHUNG, K. L. (1960). Markov Chains with Stationary Transition Probabilities. Springer, Berlin.
4. DHAR, D. (1990). Self organised critical state of sandpile automaton models. Phys. Rev. Lett. 64 1613-1616.
5. DHAR, D. (1999). The Abelian sandpiles and related models. Phys. A 263 4-25.
6. DHAR, D. and MAJUMDAR, S. N. (1990). Abelian sandpile models on the Bethe lattice J. Phys. A 23 4333-4350.
7. IVASHKEVICH, E. V. and PRIEZZHEV, V. B. (1998). Introduction to the sandpile model. Phys. A 254 97-116.
8. LIGGETT, T. M. (1980). The long range exclusion process. Ann. Probab. 8 861-889.
9. LIGGETT, T. M. (1985). Interacting Particle Systems. Springer, Berlin.
10. MAES, C., REDIG, F., SAADA E. and VAN MOFFAERT, A. (2000). On the thermodynamic limit for a one-dimensional sandpile process. Markov Process. Related Fields 6 1-22.
11. MEESTER, R., REDIG, F. and ZNAMENSKI, D. (2002). The Abelian sandpile; a mathematical introduction. Markov Process. Related Fields 7 509-523.
12. SPEER, E. (1993). Asymmetric Abelian sandpile models. J. Statist. Phys. 71 61-74.
13. STRASSEN, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36 423-439.
14. TOOM, A. L., VASILYEV, N. B., STAVSKAYA, O. N., MITYUSHIN, L. G., KURDYUMOV, G. L. and PIROGOV, S. A. (1990). Discrete local Markov systems. In Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis (R. L. Dobrushin, V. I. Kryukov and A. L. Toom, eds.) 1-182. Manchester Univ. Press.
15. TURCOTTE, D. L. (1999). Self-organized criticality. Rep. Progr. Phys. 62 1377-1429.