On a coloured tree with non i.i.d. random labels
(2010) In Statistics and Probability Letters 80(2324). p.18961903 Abstract
 We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a ddary 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 ddary 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4359863
 author
 Michael, Skevi and Volkov, Stanislav ^{LU}
 publishing date
 2010
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Branching random walks, Firstpassage percolation, Random environment on trees
 in
 Statistics and Probability Letters
 volume
 80
 issue
 2324
 pages
 1896  1903
 publisher
 Elsevier
 external identifiers

 scopus:77958511024
 ISSN
 01677152
 DOI
 10.1016/j.spl.2010.08.017
 language
 English
 LU publication?
 no
 id
 038c8ee51db247b3870539f116509106 (old id 4359863)
 date added to LUP
 20140317 14:44:04
 date last changed
 20190508 02:15:30
@article{038c8ee51db247b3870539f116509106, abstract = {We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a ddary 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 = {01677152}, keyword = {Branching random walks,Firstpassage percolation,Random environment on trees}, language = {eng}, number = {2324}, pages = {18961903}, 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}, }