Abstract
In this paper, we investigate the expectation of the size of the largest table in an (α, θ)-Chinese restaurant process by using and developing an idea originated in the work by Shepp, which discusses random permutation.
Similar content being viewed by others
References
Shepp L A, Lloyd S P. Ordered cycle lengths in random permutations. Trans Amer Math Soc, 121: 340–357 (1966)
Kolchin V F. Random Mappings. New York: Optimization Software, 1986
Bollobas B. Random Graphs, 2nd ed. Cambridge: Cambridge University Press, 2001
Pitman J. Combitorial Stochastic Processes. New York: Springer-Verlag, 2006
Chen X, Ying J. The Markov chain asymtotics of random mapping graphs. Ann Inst Henri Poincare Probab Stat, 43: 353–374 (2007)
Chen X, Ying J. Asymptotic local image of random mapping graphs. Preprint, 2009
Perman M. Order statistics for jumps of normalised subordinators. Stochastic Process Appl, 46: 267–281 (1993)
Quine M P. A calculus-based proof of a Stirling formula for the gamma function. Internat J Math Ed Sci Tech, 28: 914–917 (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by National Natural Science Foundation of China (Grant No. 10671036) and the National Basic Research Program of China (Grant No. 2007CB814904)
Rights and permissions
About this article
Cite this article
Chen, X., Ying, J. The largest table in Chinese restaurant processes. Sci. China Ser. A-Math. 52, 1569–1578 (2009). https://doi.org/10.1007/s11425-009-0101-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-009-0101-z