Free Access
Volume 17, 2013
Page(s) 531 - 549
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. [CrossRef] [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. [CrossRef] [MathSciNet] [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.