## Which Values of the Volume Growth and Escape Time Exponent Are Possible for a Graph? (2001)

by
Martin T. Barlow

Citations: | 24 - 3 self |

### BibTeX

@MISC{Barlow01whichvalues,

author = {Martin T. Barlow},

title = {Which Values of the Volume Growth and Escape Time Exponent Are Possible for a Graph?},

year = {2001}

}

### OpenURL

### Abstract

Let \Gamma = (G; E) be an infinite weighted graph which is Ahlfors ff-regular, so that there exists a constant c such that c , where V (x; r) is the volume of the ball centre x and radius r. Define the escape time T (x; r) to be the mean exit time of a simple random walk on \Gamma starting at x from the ball centre x and radius r. We say \Gamma has escape time exponent fi ? 0 if there exists a constant c such that c T (x; r) cr for r 1. Well known estimates for random walks on graphs imply that ff 1 and 2 fi 1 + ff.