M. Aizenman and T. A. Bak, Convergence to equilibrium in a system of reacting polymers, Communications in Mathematical Physics, vol.21, issue.I-1, pp.203-230, 1979.
DOI : 10.1007/BF01197880

D. Aldous, The Continuum random tree II: an overview, Stochastic analysis, pp.23-70, 1990.
DOI : 10.1017/CBO9780511662980.003

D. Aldous, The Continuum Random Tree. I, The Annals of Probability, vol.19, issue.1, pp.248-289, 1993.
DOI : 10.1214/aop/1176990534

G. E. Andrews, R. Askey, and R. Roy, Special functions, volume 71 of Encyclopedia of Mathematics and its Applications, 1999.

P. Bak, C. Tang, and K. Wiesenfeld, noise, Physical Review Letters, vol.59, issue.4, pp.381-384, 1103.
DOI : 10.1103/PhysRevLett.59.381

J. Van-den, A. A. Berg, and . Járai, On the asymptotic density in a one-dimensional self-organized critical forest-fire model, Comm. Math. Phys, vol.253, issue.3, pp.633-644, 2005.

X. Bressaud and N. Fournier, On the invariant distribution of a one-dimensional avalanche process, The Annals of Probability, vol.37, issue.1, pp.48-77, 2009.
DOI : 10.1214/08-AOP396

URL : https://hal.archives-ouvertes.fr/hal-00731532

X. Bressaud and N. Fournier, Asymptotics of one-dimensional forest fire processes, The Annals of Probability, vol.38, issue.5, pp.1783-1816, 2010.
DOI : 10.1214/09-AOP524

URL : https://hal.archives-ouvertes.fr/hal-00629372

X. Bressaud and N. Fournier, One-dimensional general forest fire processes, volume 132 of Mémoires de la Société Mathématique de France, Nouvelle Série. Soc. Math. Fr, 2013.

X. Bressaud and N. Fournier, Mean-field forest-fire models and pruning of random trees, Mém. Soc. Math. Fr. page To appear, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00731696

R. Brouwer and J. Pennanen, The Cluster Size Distribution for a Forest-Fire Process on $Z$, Electronic Journal of Probability, vol.11, issue.0, pp.1133-1143, 2006.
DOI : 10.1214/EJP.v11-369

J. Carr, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.108, issue.3-4, pp.231-244, 1992.
DOI : 10.1007/BF01197880

D. A. Darling, On the Supremum of a Certain Gaussian Process, The Annals of Probability, vol.11, issue.3, pp.803-806, 1983.
DOI : 10.1214/aop/1176993527

M. Deaconu and E. Tanré, Smoluchowski's coagulation equation: probabilistic interpretation of solutions for constant, additive and multiplicative kernels, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), vol.29, issue.3, pp.549-579, 2000.

B. Drossel and F. Schwabl, Self-organized critical forest-fire model, Physical Review Letters, vol.69, issue.11, pp.1629-1632, 1992.
DOI : 10.1103/PhysRevLett.69.1629

P. B. Dubovski?-i and I. W. Stewart, Trend to equilibrium for the coagulationfragmentation equation, Math. Methods Appl. Sci, vol.19, issue.10, pp.761-772, 1996.

S. Finch, Bessel function zeroes Unpublished, avalaible on http, 2003.

S. Finch, Airy function zeroes Unpublished, avalaible on http, 2004.

N. Fournier and S. Mischler, Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2049, pp.2477-2486, 2004.
DOI : 10.1098/rspa.2004.1294

URL : https://hal.archives-ouvertes.fr/hal-00147612

G. Grimmett, Percolation, 1989.

C. L. Henley, Self-organized percolation: a simpler model, Bull. Am. Phys. Soc, vol.34, p.838, 1989.

S. Janson, Brownian excursion area, Wright???s constants in graph enumeration, and other Brownian areas, Probability Surveys, vol.4, issue.0, pp.80-145, 2007.
DOI : 10.1214/07-PS104

G. Louchard, The brownian excursion area: a numerical analysis, Computers & Mathematics with Applications, vol.10, issue.6, pp.413-417, 1984.
DOI : 10.1016/0898-1221(84)90071-3

R. Lyons, R. Pemantle, and Y. Peres, Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes, The Annals of Probability, vol.23, issue.3, pp.1125-1138, 1995.
DOI : 10.1214/aop/1176988176

B. Ráth and B. Tóth, Erdos-Renyi random graphs + forest fires = self-organized criticality, Electronic Journal of Probability, vol.14, issue.0, pp.1290-1327, 2009.
DOI : 10.1214/EJP.v14-653

D. Revuz and M. Yor, Continuous martingales and Brownian motion, volume 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999.

S. Richard and E. W. Weisstein, Catalan number (2014) From MathWorld, A Wolfram Web Resource

P. Whittle, Systems in stochastic equilibrium Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, 1986.