Details
| Original language | English |
|---|---|
| Article number | 37 |
| Pages (from-to) | 1-22 |
| Number of pages | 22 |
| Journal | Electronic journal of probability |
| Volume | 20 |
| Publication status | Published - 2015 |
Abstract
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob- Martin compactification; it also gives a representation of the limit in terms of the input sequence of the algorithm. We further show that this approach can be used to obtain strong limit theorems for various tree functionals, such as path length or the Wiener index.
Keywords
- Doob-Martin compactification, Harris trees, Markov chains, Path length, Random trees, Wiener index
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Electronic journal of probability, Vol. 20, 37, 2015, p. 1-22.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Random recursive trees
T2 - a boundary theory approach
AU - Grübel, Rudolf
AU - Michailow, Igor
N1 - Publisher Copyright: © 2015 University of Washington. All right reserved.
PY - 2015
Y1 - 2015
N2 - We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob- Martin compactification; it also gives a representation of the limit in terms of the input sequence of the algorithm. We further show that this approach can be used to obtain strong limit theorems for various tree functionals, such as path length or the Wiener index.
AB - We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob- Martin compactification; it also gives a representation of the limit in terms of the input sequence of the algorithm. We further show that this approach can be used to obtain strong limit theorems for various tree functionals, such as path length or the Wiener index.
KW - Doob-Martin compactification
KW - Harris trees
KW - Markov chains
KW - Path length
KW - Random trees
KW - Wiener index
UR - http://www.scopus.com/inward/record.url?scp=84934873570&partnerID=8YFLogxK
U2 - 10.1214/EJP.v20-3832
DO - 10.1214/EJP.v20-3832
M3 - Article
AN - SCOPUS:84934873570
VL - 20
SP - 1
EP - 22
JO - Electronic journal of probability
JF - Electronic journal of probability
SN - 1083-6489
M1 - 37
ER -