Download this PDF file Fullscreen Fullscreen Off
References
- P. Bak. How nature works. The science of self-organized criticality. Copernicus, New York, 1996. xiv+212 pp. ISBN: 0-387-94791-4; 0-387-98738-X MR1417042
- P. Bak, C. Tang, and K. Wiesenfeld. Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59 (1987), no. 4, 381-344.
- X. Bressaud and N. Fournier. Asymptotics of one-dimensional forest fire processes. Ann. Probab. 38 (2010), no. 5, 1783-1816. MR2722786
- X. Bressaud and N. Fournier. One-dimensional general forest fire processes. arXiv:1101.0480, 2011.
- J. T. Chayes and L. Chayes. Critical points and intermediate phases on wedges of ${\bf Z}^ d$. J. Phys. A 19 (1986), no. 15, 3033-3048. MR0861221
- B. Drossel and F. Schwabl. Self-organized critical forest-fire model. Phys. Rev. Lett. 69 (1992), no. 11, 1629-1632.
- M. Dürre. Existence of multi-dimensional infinite volume self-organized critical forest-fire models. Electron. J. Probab. 11 (2006), no. 21, 513-539 (electronic). MR2242654
- M. Dürre. Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models. Electron. Comm. Probab. 11 (2006), 304-315 (electronic). MR2266720
- M. Dürre. Self-organized critical phenomena. Forest fire and sandpile models. PhD thesis, LMU München, 2009.
- G. Grimmett. Bond percolation on subsets of the square lattice, and the threshold between one-dimensional and two-dimensional behaviour. J. Phys. A 16 (1983), no. 3, 599-604. MR0701479
- G. Grimmett. Percolation. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6 MR1707339
- H. J. Jensen. Self-organized criticality. Emergent complex behavior in physical and biological systems. Cambridge Lecture Notes in Physics, 10. Cambridge University Press, Cambridge, 1998. xiv+153 pp. ISBN: 0-521-48371-9 MR1689042
- T. M. Liggett. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231
- B. Ráth and B. Tóth. Erdös-Rényi random graphs + forest fires = self-organized criticality. Electron. J. Probab. 14 (2009), no. 45, 1290-1327 (electronic). MR2511285
- A. N. Shiryayev. Probability. Translated from the Russian by R. P. Boas. Graduate Texts in Mathematics, 95. Springer-Verlag, New York, 1984. xi+577 pp. ISBN: 0-387-90898-6 MR0737192
- A. Stahl. Existence of a stationary distribution for multi-dimensional infinite volume forest-fire processes. arXiv:1203.5533, 2012.
- J. van den Berg and R. Brouwer. Self-destructive percolation. Random Structures Algorithms 24 (2004), no. 4, 480-501. MR2060632
- J. van den Berg and R. Brouwer. Self-organized forest-fires near the critical time. Comm. Math. Phys. 267 (2006), no. 1, 265-277. MR2238911
This work is licensed under a Creative Commons Attribution 3.0 License.