Teles, András Local sub-Gaussian estimates on graphs: The strongly recurrent case. (English) Zbl 1010.82020 Electron. J. Probab. 6, Paper No. 22, 33 p. (2001). Summary: This paper proves upper and lower off-diagonal, sub-Gaussian transition probabilities estimates for strongly recurrent random walks under sufficient and necessary conditions. Several equivalent conditions are given showing their particular role and influence on the connection between the sub-Gaussian estimates, parabolic and elliptic Harnack inequality. Cited in 2 Documents MSC: 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:random walks; potential theory; Harnack inequality; reversible Markov chains PDFBibTeX XMLCite \textit{A. Teles}, Electron. J. Probab. 6, Paper No. 22, 33 p. (2001; Zbl 1010.82020) Full Text: EuDML EMIS