J. F. C. Kingman, Random partitions in population genetics, Proc. Roy. Soc. London A. 361 (1978), 1--20.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....27, 1997 1 Introduction Partitions and compositions of integers are, besides their intrinsic interests, usually used as theoretical models for evolutionary processes in different contexts: statistical mechanics, theory of quantum strings, population biology, nonparametric statistics, etc. cf. [1, 4, 8, 10, 12, 30, 49, 54]. Also parameters in partitions often have natural interpretations in terms of characters in symmetric groups; cf. 15, 47] Thus properties (statistical, algebraic, analytic, of these objects received constant attention in the literature. In many situations, the notion of degree of ....

J. F. C. Kingman. Random partitions in population genetics. Proceedings of the Royal Society of London, A 361 (1978) 1--20.

....27, 1997 1 Introduction Partitions and compositions of integers are, besides their intrinsic interests, usually used as theoretical models for evolutionary processes in di#erent contexts: statistical mechanics, theory of quantum strings, population biology, nonparametric statistics, etc. cf. [1, 4, 8, 10, 12, 30, 49, 54]. Also parameters in partitions often have natural interpretations in terms of characters in symmetric groups; cf. 15, 47] Thus properties (statistical, algebraic, analytic, of these objects received constant attention in the literature. In many situations, the notion of degree of ....

J. F. C. Kingman. Random partitions in population genetics. Proceedings of the Royal Society of London, A 361 (1978) 1--20.

....[6] In the special case = 1 the Theorem is equivalent to Schoenberg s conjecture on totally positive sequences, proved in [1] 3] and to a theorem by E. Thoma [23] describing the characters of the infinite symmetric group. The limiting case = 0, in a different form, was studied by Kingman [11], see also [5] Yet another particular case where the Theorem was already known to be true is that of = 1=2. In this case it admits a representation theoretical interpretation, see [18] 21] Theorem A can be restated in terms of discrete potential theory. In this form it provides a ....

.... ( m k ( 4.1) where k denotes the length of the row of the diagram containing a box to be removed from in order to obtain , and m k ( is the total number of rows of length k in the diagram (see Fig. 2) Motivated by a problem of population genetics, J. F. C. Kingman introduced in [11] the notion of partition structure. It can be defined as a family fMng n=1 where Mn is a central (i.e. constant on conjugacy classes) probability distribution on the symmetric group Sn . The family is assumed to be coherent in the sense that d(Mn 1 ) Mn , for all n = 1; 2; where the ....

[Article contains additional citation context not shown here]

J. F. C. Kingman, Random partitions in population genetics, Proc. Roy. Soc. London A. 361 (1978), 1--20.

....foe k g, k 1 do exist. The projection of a K invariant measure on X onto the simplex Sigma of such sequences is called its radial part, and it determines the initial measure completely. The radial parts of the measures t are known as Poisson Dirichlet distributions, they were studied in [1,3,9,10]. 2. The generalized regular representations. Let z 2 C n f0g and t = jzj 2 . Using (1) one can define a unitary representation T z of the group G in the Hilbert space H = L 2 (X; t ) by the formula (T z (g)f) x) f(xg)z c(x;g) g 2 G; f 2 H: 2) We refer to T z as the generalized ....

Kingman, Random partitions in population genetics, Proc.Roy.Soc.London Ser. A 361 (1978), 1-20.

....Kingman s branching. are positive. The graph of the branching is the ordinary Young lattice, and the multiplicity (4.5) ae j ( equals the number of rows of length j in a Young diagram , assuming the box n is deleted from a row of length j in . The branching K = Y; was studied in [12], and we call it Kingman s branching (Fig. 4) S. KEROV 9 Example C (Jack s branching) The algebra R is the same as above. Let P (x; be the notation for zonal (Jack) symmetric polynomials with the parameter 0. We briefly recall the definition of Jack polynomials. Define a scalar product ....

....is coherent. Vice versa, for every coherent system of probability distributions, the function ( Mn ( d( where n 0 and 2 Gamma n , is harmonic with respect to ( Gamma; and determines via (6.6) a central Markov chain. In the particular example of Kingman s branching considered in [12], the coherent systems were called partition structures. 7. The boundary of a branching Let us start by recalling the classical integral representation of conventional harmonic functions in the disc. Denote by u = u(z) a positive harmonic function in the unit disc D = fz : jzj 1g, normalized ....

[Article contains additional citation context not shown here]

J. F. C. Kingman, Random partitions in population genetics, Proc. R. Soc. Lond. A. 361 (1978), 1-20.

....[2] In a number of subsequent papers ( 1, 3, 7] the properties of this space were studied. The study of central distributions on the space of virtual permutations, i.e. distributions that are invariant under the diagonal subgroup H of G, is parallel to Kingman s theory of partition structures ([4, 5, 6]) In particular, ergodic H invariant measures are indexed with the points of the infinite dimensional simplex. This allows one to translate to the simplex the action of the infinite symmetric group S1 on the space of virtual permutations S 1 . The result is a family of Markovian operators, and ....

....is called the Ewens measure with parameter 1. It is clear that this measure is central, and moreover, it is invariant under the whole group G. The problem of describing all central measures on the space of virtual permutations is parallel to Kingman s theory of partition structures (see [4, 5, 6]) In fact, Kingman considered coherent sequences of random partitions defined on an abstract probability space (using Kolmogorov s theorem) The space of virtual permutations gives a very natural and convenient realization of this abstract space. In this paper we do not discuss in details this ....

J. F. C. Kingman, Random partitions in population genetics, Proc. R. Soc. Lond. (A) 361 (1978), 1--20.

.... points of a Poisson point process with intensity (dx) on (0; 1) as obtained by ranking the jumps of a subordinator ( t ; 0 t 1) that is an increasing process with stationary independent increments, with E exp( Gamma s ) exp Gammas Z 1 0 (1 Gamma e Gammax ) dx) for 0: i)[22, 23] If (dx) x Gamma1 e Gammax dx for 0, corresponding to 1 with the gamma( distribution P( 1 2 dx) Gamma( Gamma1 x Gamma1 e Gammax dx, then V has PD(0; distribution. ii) 30] If (dx) cx Gammaff Gamma1 dx for ff 2 (0; 1) and c 0, corresponding to 1 with a ....

J. F. C. Kingman. Random partitions in population genetics. Proc. R. Soc. Lond. A., 361:1--20, 1978.

No context found.

J. F. C. Kingman, Random partitions in population genetics, Proc. Roy. Soc. London A. 361 (1978), 1--20.

No context found.

J. F. C. Kingman, Random partitions in population genetics, Proc. R. Soc. Lond. (A) 361 (1978), 1-20.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC