Limit laws for UGROW random graphs

Anthony Pakes

doi:10.1016/j.spl.2013.08.008

Limit laws for UGROW random graphs

Anthony Pakes

UWA Business School

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

Representations are found for a limit law L (. Z (. k, p) ) obtained from an expanding sequence of random forests containing n nodes with p ∈ (0, 1] a probability controlling bond formation. One implies that Z (. k, p) is stochastically decreasing as k increases and that norming gives an exponential limit law. Limit theorems are given for the order of component trees. The proofs exploit properties of the gamma function. © 2013 Elsevier B.V.

Original language	English
Pages (from-to)	2607-2614
Journal	Statistics and Probability Letters
Volume	83
Issue number	12
DOIs	https://doi.org/10.1016/j.spl.2013.08.008
Publication status	Published - 2013

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title = "Limit laws for UGROW random graphs",

abstract = "Representations are found for a limit law L (. Z (. k, p) ) obtained from an expanding sequence of random forests containing n nodes with p ∈ (0, 1] a probability controlling bond formation. One implies that Z (. k, p) is stochastically decreasing as k increases and that norming gives an exponential limit law. Limit theorems are given for the order of component trees. The proofs exploit properties of the gamma function. {\textcopyright} 2013 Elsevier B.V.",

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AB - Representations are found for a limit law L (. Z (. k, p) ) obtained from an expanding sequence of random forests containing n nodes with p ∈ (0, 1] a probability controlling bond formation. One implies that Z (. k, p) is stochastically decreasing as k increases and that norming gives an exponential limit law. Limit theorems are given for the order of component trees. The proofs exploit properties of the gamma function. © 2013 Elsevier B.V.

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DO - 10.1016/j.spl.2013.08.008

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