Journal of the Australian Mathematical
Society
J. Aust. Math. Soc.
1446-7887
JAUMA2
2007
83
1
10.wxyz/CV83P1
http://www.austms.org.au/Journal+of+the+Australian+Mathematical+Society/V83P1/
Rate of escape of random walks on free
products
Lorenz A. Gilch
13 February 2008
2008
2
13
31
54
831-s110-Gilch-2007
10.wxyz/C2007V83P1p31
http://www.austms.org.au/Journal+of+the+Australian+Mathematical+Society/V83P1/831-s110-Gilch/
Suppose we are given the free product $V$ of a
finite family of finite or countable sets $(V_i)_{i\in
\mathcal {I}}$ and probability measures on each $V_i$, which
govern random walks on it. We consider a transient random
walk on the free product arising naturally from the random
walks on the $V_i$. We prove the existence of the rate of
escape with respect to the block length, that is, the speed
at which the random walk escapes to infinity, and furthermore
we compute formulae for it. For this purpose, we present
three different techniques providing three different,
equivalent formulae.
primary 60G50; secondary 20E06,
60B15
MR2354???