Subexponential interval graphs generated by immigration–death processes

  • Authors:

  • Naoto Miyoshi;Mariko Ogura;Takeya Shigezumi;Ryuhei Uehara

  • Affiliations:

  • Department of mathematical and computing sciences, tokyo institute of technology, tokyo, japan e-mail: miyoshi@is.titech.ac.jp;Department of mathematical and computing sciences, tokyo institute of technology, tokyo, japan e-mail: miyoshi@is.titech.ac.jp;Department of mathematical and computing sciences, tokyo institute of technology, tokyo, japan e-mail: miyoshi@is.titech.ac.jp;School of information science, japan advanced institute of science and technology, tokyo, japan

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We propose a simple model of random interval graphs generated by immigration–death processes (also known as M/G/∞ queuing processes), where the length of each interval follows a subexponential distribution, and provide a condition under which the stationary degree distribution is also subexponential. Furthermore, we consider the conditional expectation of the cluster coefficient of a vertex given the degree and show that it vanishes in the limit as the degree goes to infinity under the same condition as that for obtaining the tail asymptotics of the stationary degree distribution.