Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the pth power of the in-degree of b. We restrict to the super-linear case p > 1. When (Formula presented), the structure of the final countable tree is determined. There is a finite tree T with distinguished v (which has a limiting distribution) on which is “glued” a specific infinite tree; v has an infinite number of children, an infinite number of which have k − 1 children, and there are only a finite number of nodes (possibly only v) with k or more children. Our basic technique is to embed the discrete process in a continuous time process using exponential random variables, a technique that has previously been employed in the study of balls-in-bins processes with feedback.
Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
John S. Lew
Mathematical Biosciences
Imran Nasim, Michael E. Henderson
Mathematics
Igor Devetak, Andreas Winter
ISIT 2003