On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models

Details On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models

2007-07-06

arxiv.org/abs/0707.0997v2

Physics

Mathematical Physics

34 pages, 8 figures

Scientific paper

10.1007/s00220-008-0533-2

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian, we introduce two families of discrete matrix models constructed both with the help of the Erdos-Renyi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogs of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions in the cases of constant and vanishing edge probabilities as n tends to infinity.

Affiliated with

Also associated with

No associations

Rating

On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-90695