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References

  1. Aldous, David. Tree-valued Markov chains and Poisson-Galton-Watson distributions. 1--20, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 41, Amer. Math. Soc., Providence, RI, 1998. MR1630406 (99k:60212)
  2. Aldous, David J. Deterministic and stochastic models for coalescence (aggregation and Bernoulli 5 (1999), no. 1, 3--48. MR1673235 (2001c:60153)
  3. Deaconu, Madalina; Fournier, Nicolas. Probabilistic approach of some discrete and continuous coagulation Stochastic Process. Appl. 101 (2002), no. 1, 83--111. MR1921443 (2003e:60152)
  4. Eibeck, Andreas; Wagner, Wolfgang. Stochastic particle approximations for Smoluchoski's coagulation Ann. Appl. Probab. 11 (2001), no. 4, 1137--1165. MR1878293 (2002k:60208)
  5. Eibeck, Andreas; Wagner, Wolfgang. Stochastic interacting particle systems and nonlinear kinetic Ann. Appl. Probab. 13 (2003), no. 3, 845--889. MR1994039 (2004d:60248)
  6. Ernst, M.H., Ziff, R.M., and Hendriks, E.M. (1984). Coagulation processes with a phase transition. J. Colloid Interface Sci. 97,1, 266--277.
  7. Escobedo, M.; Laurençot, Ph.; Mischler, S.; Perthame, B. Gelation and mass conservation in coagulation-fragmentation J. Differential Equations 195 (2003), no. 1, 143--174. MR2019246 (2004k:82069)
  8. Escobedo, M.; Mischler, S.; Perthame, B. Gelation in coagulation and fragmentation models. Comm. Math. Phys. 231 (2002), no. 1, 157--188. MR1947695 (2003m:82053)
  9. Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085 (88a:60130)
  10. Flory, P.J. (1941). Molecular size distribution in three dimensional polymers. I. Gelation. J. Am. Chem. Soc. 63, 3083--3090.
  11. Flory, P.J. (1946). Fundamental principles of condensation polymerization. Chem. Revs. 39, 137--197.
  12. Flory, P.J. (1953). Principles of polymer chemistry. Cornell University Press, New York.
  13. Fournier, Nicolas; Giet, Jean-Sébastien. Convergence of the Marcus-Lushnikov process. Methodol. Comput. Appl. Probab. 6 (2004), no. 2, 219--231. MR2035293 (2005b:60255)
  14. Gillespie, D.T. (1972). The stochastic coalescence model for cloud droplet growth. J. Atmospheric Sci. 29, 1496--1510.
  15. Guia\c s, Flavius. Convergence properties of a stochastic model for Stochastic Anal. Appl. 19 (2001), no. 2, 245--278. MR1841439 (2002d:82027)
  16. Hendriks, E. M.; Ernst, M. H.; Ziff, R. M. Coagulation equations with gelation. J. Statist. Phys. 31 (1983), no. 3, 519--563. MR0711489 (85c:82052)
  17. Herrero, M. A.; Velázquez, J. J. L.; Wrzosek, D. Sol-gel transition in a coagulation-diffusion model. Phys. D 141 (2000), no. 3-4, 221--247. MR1760997 (2001g:82073)
  18. Lang, Reinhard; Nguyen, Xuan-Xanh. Smoluchowski's theory of coagulation in colloids holds rigorously in Z. Wahrsch. Verw. Gebiete 54 (1980), no. 3, 227--280. MR0602510 (82i:60180)
  19. Laurençot, Philippe; Mischler, Stéphane. The continuous coagulation-fragmentation equations with diffusion. Arch. Ration. Mech. Anal. 162 (2002), no. 1, 45--99. MR1892231 (2003f:35166)
  20. Laurençot, Philippe; Wrzosek, Dariusz. From the nonlocal to the local discrete diffusive coagulation Math. Models Methods Appl. Sci. 12 (2002), no. 7, 1035--1048. MR1918172 (2003h:35131)
  21. Lushnikov, A.A. (1978). Certain new aspects of the coagulation theory.\newblock {\em Izv. Akad. Nauk SSSR Ser. Fiz. Atmosfer. i Okeana 14,10, 738--743.
  22. Marcus, Allan H. Stochastic coalescence. Technometrics 10 1968 133--143. MR0223151 (36 #6200)
  23. Norris, J. R. Cluster coagulation. Comm. Math. Phys. 209 (2000), no. 2, 407--435. MR1737990 (2002c:82079)
  24. Norris, J. R. Brownian coagulation. Commun. Math. Sci. 2 (2004), suppl. 1, 93--101. MR2119877 (2005k:82076)
  25. Siegmund-Schultze, Rainer; Wagner, Wolfgang. Induced gelation in a two-site spatial coagulation model. Ann. Appl. Probab. 16 (2006), no. 1, 370--402. MR2209346 (2006k:60184)
  26. Stockmayer, W.H. (1943). Theory of molecular size distribution and gel formation in branched-chain polymers. J. Chem. Phys. 11,2, 45--55.
  27. van Dongen, P. G. J. Spatial fluctuations in reaction-limited aggregation. J. Statist. Phys. 54 (1989), no. 1-2, 221--271. MR0984257 (90d:82010)
  28. van Dongen, P. G. J.; Ernst, M. H. On the occurrence of a gelation transition in Smoluchowski's J. Statist. Phys. 44 (1986), no. 5-6, 785--792. MR0858257 (87g:82019)
  29. van Dongen, P. G. J.; Ernst, M. H. Fluctuations in coagulating systems. J. Statist. Phys. 49 (1987), no. 5-6, 879--926. MR0935480 (90f:82015)
  30. von Smoluchowski, M. (1916). Drei Vortr\"age \"uber Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Phys.Z. 17, 557--571, 585--599.
  31. Wagner, Wolfgang. Explosion phenomena in stochastic coagulation-fragmentation Ann. Appl. Probab. 15 (2005), no. 3, 2081--2112. MR2152254 (2006a:60152)
  32. Ziff, Robert M. Kinetics of polymerization. J. Statist. Phys. 23 (1980), no. 2, 241--263. MR0586509 (81g:82046)
  33. Lieb, Elliott H. Comment on: "Approach to equilibrium of a Boltzmann-equation Phys. Rev. Lett. 48 (1982), no. 15, 1057. MR0650031 (84k:82059)
  34. Ziff, R.M. and Stell, G. (1980). Kinetics of polymer gelation. J. Chem. Phys. 73,7, 3492--3499.
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