<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L<sup>2</sup> and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.</p>
</abstract>

In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L2 and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.

Limit laws for two distance-based indices in random recursive tree models

Department of Statistics, Science and Research Branch

Department of Statistics, Faculty of Basic Sciences

Imam Khomeini International University Qazvin

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Limit laws for two distance-based indices in random recursive tree models"}

In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the...

Limit laws for two distance-based indices in random recursive tree models

Published Online: Aug 12, 2022

Page range: 35 - 48

Received: Feb 12, 2022

Accepted: Apr 14, 2022

DOI: https://doi.org/10.2478/ausi-2022-0003

Keywords
recursive trees, Sackin index, total path length, contraction method, martingale

© 2022 Sarkoat Naderi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Limit laws for two distance-based indices in random recursive tree models

Published Online: Aug 12, 2022

Page range: 35 - 48

Received: Feb 12, 2022

Accepted: Apr 14, 2022

DOI: https://doi.org/10.2478/ausi-2022-0003

Keywordsrecursive trees, Sackin index, total path length, contraction method, martingale

© 2022 Sarkoat Naderi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
recursive trees, Sackin index, total path length, contraction method, martingale