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arXiv:1502.07315math.PR

A Note on Diffusion State Distance

Neal Madras

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Abstract

Diffusion state distance (DSD) is a metric on the vertices of a graph, motivated by bioinformatic modeling. Previous results on the convergence of DSD to a limiting metric relied on the definition being based on symmetric or reversible random walk on the graph. We show that convergence holds even when the DSD is based on general finite irreducible Markov chains. The proofs rely on classical potential theory of Kemeny and Snell.

arXiv comments
7 pages
Journal reference
DOI
Subjects
math.PRProbability

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Linked by 1 identifiable commenter in 2 comments across 2 threads, from Jan 2016 to Jul 2016.

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  1. Does 1+2+3+... Really Equal -1/12? 1 comment

    • Glad SciAm is helping to spread correct info. I think that basically, the problem with many math videos in this style is that they tend to make uncommon, if interesting, assumptions without explaining what they are or why they make the assumption in order to get clicks. This is…

      owenversteegView on HNParent context

  2. Twitter Considering 10,000-Character Limit for Tweets 1 comment

    • "The sum of the series 1+2+3+4+5+6... = -1/12" is patently false, without a previous assertion that we have assumed the Cesàro sum of a series is equal to the series. Even mathematicians working with Cesàro sums surround such statements with "this holds only if we interpret the…

      owenversteegView on HNParent context

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