### Abstract

A bipartite random mapping T_{K,L} of a finite set V = V_{1} ? V_{2}, |V_{1}/, = K and /V_{2}/ = L, into itself assigns independently to each i ? V_{1} its unique image j ? V_{2} with probability 1/L and to each i ? V_{2} its unique image j ? V_{1} with probability 1/K. We study the connected component structure of a random digraph G(T_{K, L}), representing T_{K, L,}, as K ? 8 and L ? 8. We show that, no matter how K and L tend to infinity relative to each other, the joint distribution of the normalized order statistics for the component sizes converges in distribution to the Poisson-Dirichlet distribution on the simplex ? = {{x_{i}}: S x_{i} = 1, x_{i} = x_{i+1} = 0 for every i = 1}. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17, 317-342, 2000.

Original language | English |
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Pages (from-to) | 317-342 |

Number of pages | 26 |

Journal | Random Structures and Algorithms |

Volume | 17 |

Issue number | 3-4 |

Publication status | Published - Oct 2000 |

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### Cite this

*Random Structures and Algorithms*,

*17*(3-4), 317-342.

}

*Random Structures and Algorithms*, vol. 17, no. 3-4, pp. 317-342.

**Large components of bipartite random mappings.** / Hansen, Jennie; Jaworski, Jerzy.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Large components of bipartite random mappings

AU - Hansen, Jennie

AU - Jaworski, Jerzy

PY - 2000/10

Y1 - 2000/10

N2 - A bipartite random mapping TK,L of a finite set V = V1 ? V2, |V1/, = K and /V2/ = L, into itself assigns independently to each i ? V1 its unique image j ? V2 with probability 1/L and to each i ? V2 its unique image j ? V1 with probability 1/K. We study the connected component structure of a random digraph G(TK, L), representing TK, L,, as K ? 8 and L ? 8. We show that, no matter how K and L tend to infinity relative to each other, the joint distribution of the normalized order statistics for the component sizes converges in distribution to the Poisson-Dirichlet distribution on the simplex ? = {{xi}: S xi = 1, xi = xi+1 = 0 for every i = 1}. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17, 317-342, 2000.

AB - A bipartite random mapping TK,L of a finite set V = V1 ? V2, |V1/, = K and /V2/ = L, into itself assigns independently to each i ? V1 its unique image j ? V2 with probability 1/L and to each i ? V2 its unique image j ? V1 with probability 1/K. We study the connected component structure of a random digraph G(TK, L), representing TK, L,, as K ? 8 and L ? 8. We show that, no matter how K and L tend to infinity relative to each other, the joint distribution of the normalized order statistics for the component sizes converges in distribution to the Poisson-Dirichlet distribution on the simplex ? = {{xi}: S xi = 1, xi = xi+1 = 0 for every i = 1}. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17, 317-342, 2000.

UR - http://www.scopus.com/inward/record.url?scp=0034367938&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 317

EP - 342

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 3-4

ER -