Mathematics – Combinatorics
Scientific paper
2005-09-03
Mathematics
Combinatorics
submitted
Scientific paper
In \cite{Elek} we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph sequences. We show that in this case the integrated density of states exists that is the weak limit of the spectra of the graph Laplacians of the finite graphs is the KNS-spectral measure of the graph Laplacian of the limit graphing. Using this limit technique we prove a Cheeger type inequality for finite graphs.
No associations
LandOfFree
Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality 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 Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-382776