Exchangeable partitions derived from Markovian coalescents
نویسندگان
چکیده
منابع مشابه
Construction of Markovian Coalescents
Partition-valued and measure-valued coalescent Markov processes are constructed whose state describes the decomposition of a nite total mass m into a nite or countably in nite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of masses of magnitudes x and y runs the risk of a binary collision to form a single mass of magnitude x+y ...
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An improved condition to come down from infinity for exchangeable coalescent processes with simultaneous multiple collisions of ancestral lineages is provided. For non-critical coalescents this leads to an improved necessary and sufficient condition for the coalescent to come down from infinity. An analog conjecture for the full class of exchangeable coalescents is presented. New examples of cr...
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Call a random partition of the positive integers partially exchangeable if for each finite sequence of positive integers n l , . . . , nk, the probability that the partition breaks the first nl + . . . § nk integers into k particular classes, of sizes nl . . . . , nk in order of their first elements, has the same value p(na . . . . . nk) for every possible choice of classes subject to the sizes...
متن کاملPartially Exchangeable Random Partitions
A random partition of the positive integers is called partially exchangeable if for each finite sequence of positive integers n,, ... , nk, the probability that the partition breaks the first n1 + + nk integers into k particular classes, of sizes nl,.. . ., nk in order of their first elements, has the same value p(nl,...,nk) for every possible choice of classes subject to the sizes constraint. ...
متن کاملConstrained exchangeable partitions
Under a partition of the set N we shall mean a sequence (b1, b2, . . .) of subsets of N such that (i) the sets bj are disjoint, (ii) ∪jbj = N, (iii) if bk = ∅ then also bk+1 = ∅ and (iv) if bk+1 6= ∅ then min bk < min bk+1. Condition (iv) says that the sequence of minimal elements of the blocks is increasing. One can think of partition as a mapping which sends a generic element j ∈ N to one of ...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2007
ISSN: 1050-5164
DOI: 10.1214/105051607000000069