Uniform asymptotic estimates of transition probabilities on combs

Daniela Bertacchi, Fabio Zucca
2003 Journal of the Australian Mathematical Society  
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular, we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting sub-Gaussian estimates involving the spectral and walk dimensions of the graph. 2000 Mathematics subject classification: primary 60J10.
doi:10.1017/s1446788700008144 fatcat:bp2p5hmrovdg3prt2wioaplipe