Details
| Original language | English |
|---|---|
| Pages (from-to) | 1269-1297 |
| Number of pages | 29 |
| Journal | Annals of Applied Probability |
| Volume | 24 |
| Issue number | 3 |
| Publication status | Published - Jun 2014 |
Abstract
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Annals of Applied Probability, Vol. 24, No. 3, 06.2014, p. 1269-1297.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Search trees
T2 - Metric aspects and strong limit theorems
AU - Grübel, Rudolf
N1 - Copyright © 2014 Institute of Mathematical Statistics
PY - 2014/6
Y1 - 2014/6
N2 - We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
AB - We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
UR - http://www.scopus.com/inward/record.url?scp=84899549401&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1209.2546
DO - 10.48550/arXiv.1209.2546
M3 - Article
AN - SCOPUS:84899549401
VL - 24
SP - 1269
EP - 1297
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 3
ER -