Name
Title | ||
|---|---|---|
Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality |
Abstract | ||
|---|---|---|
In [G. Elek, On limits of finite graphs, Combinatorica, in press, URL: http://www.arxiv.org/pdf/math.CO/0505335] 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jctb.2007.03.004 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
von neumann algebras,isoperimetric inequalities,graph laplacians,cheeger type inequality,limit technique,graph sequence,integrated density,integrated density of states,finite graph,infinite graph,graph laplacian,limit graphing,type ii,weak convergence of graphs,weak convergence,weak limit,von neumann algebra,operator algebra,isoperimetric inequality | Indifference graph,Combinatorics,Forbidden graph characterization,Partial k-tree,Cheeger constant (graph theory),Pathwidth,1-planar graph,Universal graph,Mathematics,Split graph | Journal |
Volume | Issue | ISSN |
98 | 1 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
1 | 0.63 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gábor Elek | 1 | 35 | 4.13 |