Limit distribution of the degrees in scaled attachment random recursive trees

author

  • M. Javanian Department of Statistics, Zanjan University, Zanjan, Iran
Abstract:

We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor iX_i floor$ where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random variables, with support in [0, 1) and distribution function $F$. By imposing a condition on $F$, we show that the degree of a given node is asymptotically normal.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Limit Distribution of Degrees in Scaled Attachment Random Recursive Trees

We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node i is attached to the node labeled biXic where X0, . . . , Xn is a sequence of i.i.d. random variables, with support in [0, 1) and distribution fun...

full text

limit distribution of the degrees in scaled attachment random recursive trees

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...

full text

Degrees in $k$-minimal label random recursive trees

This article describes the limiting distribution of the degrees of nodes has been derived for a kind of random tree named k-minimal label random recursive tree, as the size of the tree goes to infinity. The outdegree of the tree is equal to the number of customers in a pyramid marketing agency immediatly alluring

full text

The height of scaled attachment random recursive trees

We study depth properties of a general class of random recursive trees where each node n attaches to the random node !nXn" and X0, . . . , Xn is a sequence of i.i.d. random variables taking values in [0, 1). We call such trees scaled attachment random recursive trees (SARRT). We prove that the height Hn of a SARRT is asymptotically given by Hn ∼ αmax log n where αmax is a constant depending onl...

full text

Depth Properties of scaled attachment random recursive trees

We study depth properties of a general class of random recursive trees where each node i attaches to the random node biXic and X0, . . . , Xn is a sequence of i.i.d. random variables taking values in [0, 1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the height Hn of a sarrt is asymptotically given by Hn ∼ αmax logn where αmax is a constant depending only...

full text

Limit distribution of degrees in random family trees

In a one-parameter model for evolution of random trees, which also includes the Barabási–Albert random tree [1], almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. A functional central limit theorem is also given. Results about Pólya urn models are applied in the proofs.

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 39  issue 5

pages  1031- 1036

publication date 2013-10-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023