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All issues Volume 17 (2013) ESAIM: PS, 17 (2013) 531-549 References
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Issue
ESAIM: PS
Volume 17, 2013
Page(s) 531 - 549
DOI https://doi.org/10.1051/ps/2012007
Published online 03 June 2013
  1. G. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications. Addison-Wesley 2 (1976). [Google Scholar]
  2. R. Arratia and S. Tavaré, Independent process approximations for random combinatorial structures. Adv. Math. 104 (1994) 90–154. [CrossRef] [MathSciNet] [Google Scholar]
  3. R. Arratia, A. Barbour and S. Tavaré, Logarithmic combinatorial structures: a probabilistic approach. European Mathematical Society Publishing House, Zurich (2004). [Google Scholar]
  4. A. Barbour and B. Granovsky, Random combinatorial structures: the convergent case. J. Comb. Theory, Ser. A 109 (2005) 203–220. [CrossRef] [Google Scholar]
  5. J. Bell, Sufficient conditions for zero-one laws. Trans. Amer. Math. Soc. 354 (2002) 613–630. [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Bell and S. Burris, Asymptotics for logical limit laws: when the growth of the components is in RT class. Trans. Amer. Soc. 355 (2003) 3777–3794. [CrossRef] [Google Scholar]
  7. N. Berestycki and J. Pitman, Gibbs distributions for random partitions generated by a fragmentation process. J. Stat. Phys. 127 (2006) 381–418. [CrossRef] [Google Scholar]
  8. J. Bertoin, Random fragmentation and coagulation processes, Cambridge Studies in Advanced Mathematics. Cambridge University Press (2006). [Google Scholar]
  9. B. Bollobás, Random graphs, Cambridge Studies in Advanced Mathematics. Cambridge University Press (2001). [Google Scholar]
  10. S. Burris, Number theoretic density and logical limit laws, Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI 86 (2001). [Google Scholar]
  11. S. Burris and K. Yeats, Sufficient conditions for labelled 0 − 1 laws. Discrete Math. Theory Comput. Sci. 10 (2008) 147–156. [Google Scholar]
  12. P. Cattiaux and N. Gozlan, Deviations bounds and conditional principles for thin sets. Stoch. Proc. Appl. 117 (2007) 221–250. [CrossRef] [Google Scholar]
  13. A. Dembo and O. Zeitouni, Refinements of the Gibbs conditioning principle. Probab. Theory Relat. Fields 104 (1996) 1–14. [Google Scholar]
  14. R. Durrett, B. Granovsky and S. Gueron, The equilibrium behaviour of reversible coagulation-fragmentation processes. J. Theoret. Probab. 12 (1999) 447–474. [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Diaconis and D. Freedman, Conditional limit theorems for exponential families and finite versions of de Finetti’s theorem. J. Theoret. Probab. 1 (1988) 381–410. [Google Scholar]
  16. M. Erlihson and B. Granovsky, Reversible coagulation-fragmentation processes and random combinatorial structures: asymptotics for the number of groups. Random Struct. Algorithms 25 (2004) 227–245. [CrossRef] [Google Scholar]
  17. M. Erlihson and B. Granovsky, Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and random combinatorial structures. Ann. Inst. Henri Poincaré Prob. Stat. 44 (2005) 915–945. [CrossRef] [Google Scholar]
  18. G. Freiman and B. Granovsky, Asymptotic formula for a partition function of reversible coagulation-fragmentation processes. J. Israel Math. 130 (2002) 259–279. [CrossRef] [Google Scholar]
  19. G. Freiman and B. Granovsky, Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: asymptotic formulae and limiting laws. Trans. Amer. Math. Soc. 357 (2005) 2483–2507. [CrossRef] [MathSciNet] [Google Scholar]
  20. B. Fristedt, The structure of random partitions of large integers. Trans. Amer. Math. Soc. 337 (1993) 703–735. [CrossRef] [MathSciNet] [Google Scholar]
  21. B. Granovsky and A. Kryvoshaev, Coagulation processes with Gibbsian time evolution. arXiv:1008.1027 (2010). [Google Scholar]
  22. B. Granovsky and D. Stark, Asymptotic enumeration and logical limit laws for expansive multisets. J. London Math. Soc. 73 (2005) 252–272. [CrossRef] [Google Scholar]
  23. W. Greiner, L. Neise and H. Stӧcker, Thermodinamics and Statistical Mechanics, Classical Theoretical Physics. Springer-Verlag (2000). [Google Scholar]
  24. E. Grosswald, Representatin of integers as sums of squares. Springer-Verlag (1985). [Google Scholar]
  25. F. Kelly, Reversibility and stochastic networks. Wiley (1979). [Google Scholar]
  26. V. Kolchin, Random graphs, Encyclopedia of Mathematics and its Applications. Cambridge University Press 53 (1999). [Google Scholar]
  27. J. Pitman, Combinatorial stochastic processes. Lect. Notes Math. 1875 (2006). [Google Scholar]
  28. G. Polya and G. szego, Problems and Theorems in Analysis, Vol. VI. Springer-Verlag (1970). [Google Scholar]
  29. L. Salasnich, Ideal quantum gas in D-dimensional space and power law potentials, J. Math. Phys. 41 (2000) 8016–8024. [CrossRef] [Google Scholar]
  30. D. Stark, Logical limit laws for logarithmic structures, Math. Proc. Cambridge Philos. Soc. 140 (2005) 537–544. [CrossRef] [Google Scholar]
  31. A. Vershik, Statistical mechanics of combinatorial partitions and their limit configurations. Funct. Anal. Appl. 30 (1996) 90–105. [CrossRef] [Google Scholar]
  32. A. Vershik and Yu. Yakubovich, Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions. Commun. Math. Phys. 261 (2006) 759–769. [CrossRef] [Google Scholar]
  33. P. Whittle, Systems in stochastic equilibrium. Wiley (1986). [Google Scholar]
  34. Yu. Yakubovich, Ergodicity of multiple statistics. arXiv:0901.4655v2 [math.CO] (2009). [Google Scholar]
  35. K. Yeats, A multiplicative analogue of Schur’s Tauberian theorem. Can. Math. Bull. 46 (2003) 473–480. [CrossRef] [Google Scholar]

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