Bose-Einstein condensation in random directed networks
Abstract
We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probability p and an edge with probability 1-p. The new vertex has a fitness (a,b) a,b>0, with probability f(a,b). A vertex with fitness (a,b), with in-degree i and out-degree j, gains a new incoming edge with rate a(i+1) and an outgoing edge with rate b(j+1). The Bose-Einstein condensation occurs as a function of fitness distribution f(a,b).
- Publication:
-
Physical Review E
- Pub Date:
- November 2003
- DOI:
- 10.1103/PhysRevE.68.056118
- arXiv:
- arXiv:cond-mat/0306622
- Bibcode:
- 2003PhRvE..68e6118S
- Keywords:
-
- 02.50.Cw;
- 05.40.-a;
- Probability theory;
- Fluctuation phenomena random processes noise and Brownian motion;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 3 figures, submitted for publication