ISSN:
1572-9230
Keywords:
Trees
;
random walks
;
speed
;
inequality
;
mean
;
harmonic
;
geometric
;
arithmetic
;
Jensen's Inequality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We define trees generated by bi-infinite sequences, calculate their walk-invariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-infinite sequence with a simple random walk on an augmented Galton-Watson tree. We find that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree generated by a bi-infinite sequence. This is due to an inequality for random variables with values in [1, ∞[ involving harmonic, geometric and arithmetic mean.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022602614733
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