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On a coloured tree with non i.i.d. random labels

Michael, Skevi and Volkov, Stanislav LU (2010) In Statistics and Probability Letters 80(23-24). p.1896-1903
Abstract
We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a dd-ary regular tree. All vertices are coloured in one of dd distinct colours so that dd children of each vertex all have different colours. Fix d2d2 strictly positive random variables. For any two connected vertices of the tree assign to the edge between them a label which has the same distribution as one of these random variables, such that the distribution is determined solely by the colours of its endpoints. A value of a vertex is defined as a product of all labels on the path connecting the vertex to the root. We study how the total number of vertices with value of at least xx grows as x↓0x↓0, and apply the results... (More)
We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a dd-ary regular tree. All vertices are coloured in one of dd distinct colours so that dd children of each vertex all have different colours. Fix d2d2 strictly positive random variables. For any two connected vertices of the tree assign to the edge between them a label which has the same distribution as one of these random variables, such that the distribution is determined solely by the colours of its endpoints. A value of a vertex is defined as a product of all labels on the path connecting the vertex to the root. We study how the total number of vertices with value of at least xx grows as x↓0x↓0, and apply the results to some other relevant models. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Branching random walks, First-passage percolation, Random environment on trees
in
Statistics and Probability Letters
volume
80
issue
23-24
pages
1896 - 1903
publisher
Elsevier
external identifiers
  • scopus:77958511024
ISSN
0167-7152
DOI
10.1016/j.spl.2010.08.017
language
English
LU publication?
no
id
038c8ee5-1db2-47b3-8705-39f116509106 (old id 4359863)
date added to LUP
2014-03-17 14:44:04
date last changed
2018-05-29 09:55:08
@article{038c8ee5-1db2-47b3-8705-39f116509106,
  abstract     = {We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a dd-ary regular tree. All vertices are coloured in one of dd distinct colours so that dd children of each vertex all have different colours. Fix d2d2 strictly positive random variables. For any two connected vertices of the tree assign to the edge between them a label which has the same distribution as one of these random variables, such that the distribution is determined solely by the colours of its endpoints. A value of a vertex is defined as a product of all labels on the path connecting the vertex to the root. We study how the total number of vertices with value of at least xx grows as x↓0x↓0, and apply the results to some other relevant models.},
  author       = {Michael, Skevi and Volkov, Stanislav},
  issn         = {0167-7152},
  keyword      = {Branching random walks,First-passage percolation,Random environment on trees},
  language     = {eng},
  number       = {23-24},
  pages        = {1896--1903},
  publisher    = {Elsevier},
  series       = {Statistics and Probability Letters},
  title        = {On a coloured tree with non i.i.d. random labels},
  url          = {http://dx.doi.org/10.1016/j.spl.2010.08.017},
  volume       = {80},
  year         = {2010},
}