Christiane Takacs, Roland Takacs,
"Random Walks on Trees and an Inequality of Means"
, in Journal of Theoretical Probability, Vol. 11, Seite(n) 701-714, 1998
Random Walks on Trees and an Inequality of Means
Sprache des Titels:
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,Infinity[ involving harmonic, geometric and arithmetic mean.