A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Exponential decay of connectivity and uniqueness in percolation on finite and infinite graphs
[article]
2016
arXiv
pre-print
Preserved Fulltext
We give an upper bound for the uniqueness transition on an arbitrary locally finite graph G in terms of the limit of the spectral radii ρ[ H( G_t)] of the non-backtracking (Hashimoto) matrices for an increasing sequence of subgraphs G_t⊂ G_t+1 which converge to G. With the added assumption of strong local connectivity for the oriented line graph (OLG) of G, connectivity on any finite subgraph G'⊂ G decays exponentially for p<(ρ[ H( G^')])^-1.
arXiv:1610.04897v1
fatcat:tnfdvilumbdvhdhazbbek3y5ca