How to cite item

Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities

   
@article{EJP58,
	author = {Michael Camarri and Jim Pitman},
	title = {Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {5},
	year = {1999},
	keywords = {Repeat times, point process, Poisson embedding, inhomogeneous continuum random tree, Rayleigh distribution},
	abstract = {Given an arbitrary distribution on a countable set, consider the number of  independent samples required until the first repeated value is seen.  Exact and asymptotic formulae are derived for the distribution of this time and of the times until subsequent repeats. Asymptotic properties of the repeat  times are derived by embedding in a Poisson process. In particular, necessary  and sufficient conditions for convergence are given and the possible limits  explicitly described. Under the same conditions the finite dimensional  distributions of the repeat times converge to the arrival times of suitably  modified Poisson processes, and random trees derived from the sequence of  independent trials converge in distribution to an inhomogeneous continuum  random tree.},
	pages = {no. 2, 1-18},
	issn = {1083-6489},
	doi = {10.1214/EJP.v5-58},    
        url = {http://ejp.ejpecp.org/article/view/58}}