Correction: Phase Transitions on Markovian Bipartite Graphs—an Application of the Zero-range Process (Journal of Statistical Physics, (2005), 119, 3-4, (881-907), 10.1007/s10955-005-3011-7);Phase transitions on Markovian bipartite graphs-an application of the zero-range process

Journal of Statistical Physics

Volumn 119, Issue 3-4, 2005, Pages 881-907

  Pulkkinen, Otto ^a   Merikoski, Juha ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Condensation; Giant component; Random graph; Zero range process

Indexed keywords

EID: 21644434293     PISSN: 00224715     EISSN: 15729613     Source Type: Journal    
DOI: 10.1007/s10955-023-03192-6     Document Type: Erratum

References (30)

1. B. Bollobás, Random Graphs (Academic Press, London, 1985).
2. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51:1079 (2002).
3. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286:509-512 (1999).
4. D. J. de S. Price, A general theory of bibliometric and other cumulative advantage processes, J. Am. Soc. Inform. Sci. 27:292-306 (1976).
5. F. Spitzer, Adv. Math. 5:246-290 (1970).
6. G. Palla, I. Derényi, I. Farkas, and T. Vicsek, Statistical mechanics of topological phase transitions in networks, Phys. Rev. E 69:046117 (2004).
7. B. Pittel, W. A. Woyczynski, and J. A. Mann, Random tree-type partitions as a model for acyclic polymerization: Holtsmark (3/2-stable) distribution of the supercritical gel, Ann. Prob. 18:319-341 (1990).
8. B. Pittel and W. A. Woyczynski, A graph-valued Markov process as rings-allowed polymerization model: Subcritical behavior, SIAM J. Appl. Math. 50:1200-1220 (1990).
9. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Principles of statistical mechanics of uncorrelated random networks, Nucl. Phys. 5666:396-416 (2003).
10. M. R. Evans, Brazilian J. Phys. 30: 42 (2000), e-print cond-mat/0007293.
11. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E 64:026118 (2001).
12. M. Molloy, and B. Reed, A critical point for random graphs with a given degree sequence, Random Struct. Algorithms 6:161 (1995).
13. M. Molloy, and B. Reed, The size of the giant component of a random graph with a given degree sequence, Combinatorics Probab. Comput. 7:295 (1998).
14. L→∞ P(B) = 1.
15. S. Großkinsky, G. M. Schütz, and H. Spohn, J. Stat. Phys. 113(3):389-410 (2003).
16. I. Jeon, P. March, and B. Pittel, Am. Probab. 28:1162-1194 (2000).
17. R. Arratia, and S. Tavaré, Independent process approximations for random combinatorial structures, Adv. Math. 104:90-154 (1994).
18. S. Corteel, B. Pittel, C. D. Savage, and H. S. Wilf, On the multiplicity of parts in a random partition, Random Struct. Algorithms 14:185-197 (1999).
19. P. Brémaud, Markov Chains: Gibbs Fields, Monte-Carlo Simulation, and Queues (Springer, New York, 1999).
20. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, revised edition (Addison-Wesley, Reading, 1968).
21. C. Kipnis and C. Landim, Scaling Limits of Interacting Particle Systems (Springer, Berlin, 1999).
22. T. M. Liggett, Interacting Particle Systems (Springer, Berlin, 1985).
23. T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Springer, Berlin, 1999).
24. B. Derrida and M. R. Evans, in Nonequilibrium Statistical Mechanics in One Dimension, V Privman, ed. (Cambridge University Press, Cambridge, 1997).
25. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
26. N. Alon, J. H. Spencer, and P. Erdös, The Probabilistic Method (Wiley, New York, 1991).
27. 2/N approaching zero as in the case of Fig. 3.
28. R. Cohen, D. ben-Avraham, and S. Havlin, Percolation critical exponents in scale-free networks, Phys. Rev. E 66:036113 (2002).
29. A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Critical phenomena in networks, Phys. Rev. E 67:026123 (2003).
30. C. Godrèche, Dynamics of condensation in zero-range processes, J. Phys. A: Math. Gen. 36(23):6313-6328 (2003).