Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex

@article{Donnelly1989ContinuityAW,
  title={Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex},
  author={Peter Donnelly and Paul Joyce},
  journal={Stochastic Processes and their Applications},
  year={1989},
  volume={31},
  pages={89-103}
}
  • P. Donnelly, P. Joyce
  • Published 1 March 1989
  • Mathematics
  • Stochastic Processes and their Applications
The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
The two-parameter Poisson-Dirichlet distribution, denoted PD(α,θ), is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with
Functionals of random mappings: exact and asymptotic results
A random mapping partitions the set {1, 2, ···, m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various
The heaps process, libraries, and size-biased permutations
The heaps process (also known as a Tsetlin library) provides a model for a self-regulating filing system. Items are requested from time to time according to their popularity and returned to the top
Functionals of random mappings : exact and asymptotic results
A random mapping partitions the set {1,2, o , m) into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various
A convergence theorem for symmetric functionals of random partitions
This paper gives general conditions under which symmetric functionals of random partitions of the integer rn converge in distribution as rn 03. The main result is used to settle a conjecture of
On random polynomials over finite fields
We consider random monic polynomials of degree n over a finite field of q elements, chosen with all q" possibilities equally likely, factored into monic irreducible factors. More generally, relaxing
Size-biased sampling of Poisson point processes and excursions
SummarySome general formulae are obtained for size-biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function.
FUNCTIONALS OF RANDOM MAPPINGS: EXACT AND
A random mapping partitions the set (1, 2, ,m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various
Limiting behaviour of random spatial graphs and asymptotically homogeneous RWRE
We consider several random spatial graphs of the nearest-neighbour type, including the k- nearest neighbours graph, the on-line nearest-neighbour graph, and the minimal directed spanning tree. We
GAUSSIAN LIMITS ASSOCIATED WITH THE POISSON-DIRICHLET DISTRIBUTION AND THE EWENS SAMPLING FORMULA
In this paper we consider large θ approximations for the stationary distribution of the neutral infinite alleles model as described by the the Poisson–Dirichlet distribution with parameter θ. We
...
...

References

SHOWING 1-10 OF 20 REFERENCES
Ordered cycle lengths in a random permutation
1. Introduction. Problems involving a random permutation are often concerned with the cycle structure of the permutation. Let tY.n be the n! permutation operators on n numbered places, and let a(X) =
On random discrete distributions
It is impossible to choose at random a probability distribution on a countably infinite set in a manner invariant under permutations of that set. However,approximations to such a choice can be made
The stationary distribution of the infinitely-many neutral alleles diffusion model
An expression is found for the stationary density of the allele frequencies, in the infinitely-many alleles model. It is assumed that all alleles are neutral, that there is a constant mutation rate,
The population structure associated with the Ewens sampling formula.
  • J. Kingman
  • Mathematics
    Theoretical population biology
  • 1977
Population Genetics Theory - The Past and the Future
TLDR
The retrospective theory introduces ideas not appearing in the classical theory, particularly those concerning the ancestry of the genes in a sample or in the entire population, and introduces two important new distributions into the scientific literature, namely the Poisson-Dirichlet and the GEM.
SIZE-BIASED FILTERING OF POISSON-DIRICHLET SAMPLES WITH AN APPLICATION TO PARTITION STRUCTURES IN GENETICS
A characteristic property of the Ewen sampling formula is shown to follow from the invariance under size-biased sampling of the Poisson-Dirichlet distribution.
Is the most frequent allele the oldest?
...
...