REVIEW 1 cited by
Commuting time geometry of ergodic Markov chains
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of commuting times, and from this we get monotonicity of commuting times with respect to equilibrium transition rates. All of these results are familiar in the case of time-reversible chains, where techniques of classical electrical theory apply. In presenting these results, we take the opportunity to develop Markov chain theory in a `conformally correct' way
Forward citations
Cited by 1 Pith paper
-
Thermodynamic geometry of friction on graphs: Resistance, commute times, and optimal transport
For slowly driven reversible Markov chains, the friction metric equals the graph-Laplacian pseudoinverse (resistance distance and commute-time geometry), and the thermodynamic distance is an equilibrium-restricted dis...
Discussion (0). Continue with ORCID to comment.