Stick breaking process generated by virtual permutations with Ewens distribution

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Stick breaking process generated by virtual permutations with Ewens distribution. / Kerov, S. V.; Tsilevich, N. V.

In: Journal of Mathematical Sciences , Vol. 87, No. 6, 01.01.1997, p. 4082-4093.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{d6ed65188ca4402a98098007d37b09a3,

title = "Stick breaking process generated by virtual permutations with Ewens distribution",

abstract = "Given a sequence x of points in the unit interval, we associate with it a virtual permutation w = w(x) (that is, a sequence w of permutations w n ∈ G fraktur signn such that for all n = 1, 2, . . ., wn-1 = wn l is obtained from wn by removing the last element n from its cycle). We introduce a detailed version of the well-known stick breaking process generating a random sequence x. It is proved that the associated random virtual permutation w(x) has a Ewens distribution. Up to subsets of zero measure, the space G fraktur sign ∞ = lim← G fraktur signn of virtual permutations is identified with the cube [0,1]∞.",

author = "Kerov, {S. V.} and Tsilevich, {N. V.}",

year = "1997",

month = jan,

day = "1",

doi = "10.1007/BF02355804",

language = "English",

volume = "87",

pages = "4082--4093",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Stick breaking process generated by virtual permutations with Ewens distribution

AU - Kerov, S. V.

AU - Tsilevich, N. V.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Given a sequence x of points in the unit interval, we associate with it a virtual permutation w = w(x) (that is, a sequence w of permutations w n ∈ G fraktur signn such that for all n = 1, 2, . . ., wn-1 = wn l is obtained from wn by removing the last element n from its cycle). We introduce a detailed version of the well-known stick breaking process generating a random sequence x. It is proved that the associated random virtual permutation w(x) has a Ewens distribution. Up to subsets of zero measure, the space G fraktur sign ∞ = lim← G fraktur signn of virtual permutations is identified with the cube [0,1]∞.

AB - Given a sequence x of points in the unit interval, we associate with it a virtual permutation w = w(x) (that is, a sequence w of permutations w n ∈ G fraktur signn such that for all n = 1, 2, . . ., wn-1 = wn l is obtained from wn by removing the last element n from its cycle). We introduce a detailed version of the well-known stick breaking process generating a random sequence x. It is proved that the associated random virtual permutation w(x) has a Ewens distribution. Up to subsets of zero measure, the space G fraktur sign ∞ = lim← G fraktur signn of virtual permutations is identified with the cube [0,1]∞.

UR - http://www.scopus.com/inward/record.url?scp=0039587844&partnerID=8YFLogxK

U2 - 10.1007/BF02355804

DO - 10.1007/BF02355804

M3 - Article

AN - SCOPUS:0039587844

VL - 87

SP - 4082

EP - 4093

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 49790625