The Markov chain asymptotics of random mapping graphs

 Access to full text

 Full (PDF)

1. [1] D.J. Aldous, G. Miermont, J. Pitman, Brownian bridge asymptotics for random p-mappings, Electron. J. Probab.9 (2004) 37-56. Zbl1064.60012MR2041828
2. [2] D.J. Aldous, J. Pitman, Brownian bridge asymptotics for random mappings, Random Structures Algorithms5 (1994) 487-512. Zbl0811.60057MR1293075
3. [3] W. Feller, An Introduction to Probability Theory and its Applications, vol. I, third ed., John Wiley & Sons, 1968. Zbl0155.23101MR228020
4. [4] I.B. Gertsbakh, Epidemic processes on a random graph: some preliminary results, J. Appl. Probab.14 (1977) 427-438. Zbl0373.92032MR456601
5. [5] V.F. Kolchin, Random Mappings, Optimization Software, New York, 1986, (Translation of Russian original). Zbl0605.60010MR865130
6. [6] J. Pitman, Combitorial Stochastic Processes, Lecture Notes in Math., Springer, Berlin, in press. Available now via, http://bibserver.berkeley.edu/csp/csp.html. Zbl1103.60004MR2245368
7. [7] B. Pittel, On distributions related to transitive closures of the random finite mappings, Ann. Probab.11 (1983) 428-441. Zbl0515.60015MR690140
8. [8] S. Ramanujan, Question 294, J. Indian Math. Soc.3 (1911) 128. 
9. [9] S.M. Ross, Introduction to Probability Models, seventh ed., Academic Press, 2000. Zbl0977.60001MR1766683
10. [10] L.A. Shepp, S.P. Lloyd, Ordered cycle lengths in random permutations, Trans. Amer. Math. Soc.121 (1966) 340-357. Zbl0156.18705MR195117
11. [11] V.E. Stepanov, Limit distributions of certain characteristics of random mappings, Theory Probab. Appl.14 (1969) 612-626. Zbl0193.46401MR278350
12. [12] V.E. Stepanov, Random mappings with a single attracting centre, Theory Probab. Appl.16 (1971) 155-161. Zbl0239.60017MR410842