Centers for Random Walks on Trees


We consider two distinct centers which arise in measuring how quickly a random walk on a tree mixes. Lovász and Winkler [8] point out that stopping rules which “look where they are going” (rather than simply walking a fixed number of steps) can achieve a desired distribution exactly and efficiently. Considering an optimal stopping rule that reflects some aspect of mixing, we can use the expected length of this rule as a mixing measure. On trees, a number of these mixing measures identify particular nodes with central properties. In this context, we study a variety of natural notions of centrality. Each of these criteria identifies the barycenter of the tree as the “average” center and the newly defined focus as the “extremal” center.

DOI: 10.1137/070687402

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@article{Beveridge2009CentersFR, title={Centers for Random Walks on Trees}, author={Andrew Beveridge}, journal={SIAM J. Discrete Math.}, year={2009}, volume={23}, pages={300-318} }