CoChat
Sign Up
Cited by 1,061

The DOI matches its Crossref record.

Random Walks and Electric Networks

Doyle, Peter, Snell, J.·1984·Carus Mathematical Monographs
DOI 10.5948/upo9781614440222
Open this paper in CoChat — free account

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.5948/upo9781614440222

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Doyle & Snell (1984) demonstrated that resistance distances from circuit theory are directly proportional to the movements of Markovian random walkers on graphs.

    “Specifically, Doyle & Snell (1984) demonstrated that resistance distances from circuit theory are directly proportional to the movements of Markovian random walkers on graphs, and Chandra et al. (1996) related resistance distances to “commute times,” or the time it takes a random walker to travel from one point to another and back again.”

    From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as Doyle & Snell (1984)

    Section 1.3.1 connects random walks on graphs with resistor networks and reversible Markov chains, and §1.3.4 relates effective resistance to a walker's probability of reaching one vertex before returning to another. But §1.3.4 gives that probability as proportional to effective conductance—the reciprocal of resistance—not as directly proportional to resistance. The claimed direct proportionality to the walker's “movements” is therefore not established. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Circuit theory simultaneously considers all possible pathways connecting population pairs, producing a map where current density varies across pixels and is analogous to the probability of use by random walkers.

    “Circuit theory simultaneously considers all possible pathways connecting population pairs, producing a map where current density varies across pixels and is analogous to the probability of use by random walkers (Doyle & Snell 1984).”

    From Landscape connectivity for wildlife: development and validation of multispecies linkage maps (2014) · cites this paper as Doyle & Snell 1984

    Section 1.3.2 models currents across a network between two points, and §1.3.3 relates current on each edge to random walks between those points. But §1.3.3 defines current as the expected net number of edge crossings, not the probability that a walker uses an edge. The copy does not describe population pairs, pixel maps, or current density across pixels; no page numbers are available in the supplied passages. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 14

  1. M. L. Glasser and I. J. Zucker. Extended Watson integrals for the cubic lattice. Proc. Natl. Acad. Sci., USA, 74:1800-1801, 1977.
  2. R. Hersh and R. J. Griego. Brownian motion and potential theory. Scientific American, pages 66-74, March 1969.
  3. J. Jeans. The Mathematical Theory of Electricity and Magnetism, 5th Edition. 1966.
  4. S. Kakutani. Markov processes and the Dirichlet problem. Proc. Jap. Acad., 21:227-233, 1945.
  5. J. G. Kemeny, J. L. Snell, and G. L. Thompson. Finite Markov Chains, 3rd Edition. 1974.
  6. A. Lehman. A resistor network inequality, Problem 60-5. SIAM Review, 4:150-154, 1965.
  7. J. C. Maxwell. Treatise on Electricity and Magnetism, 3rd Edition. 1891.
  8. W. H. McCrea and F. J. W. Whipple. Random paths in two and three dimensions. Proc. of the Royal Soc. of Edinburgh, 60:281- 298, 1940.
  9. E. W. Montroll and B. J. West. Fluctuation phenomena. In Studies in Statistical Mathematics, volume 7, pages 61-175. 1979.
  10. C. St. J. A. Nash-Williams. Random walk and electric currents in networks. Proc. Camb. Phil. Soc., 55:181-194, 1959.
  11. G. Polya. How to Solve It, 2nd Edition. 1957.
  12. J. W. S. Rayleigh. On the theory of resonance. In Collected sci- entific papers, volume 1, pages 33-75. 1899.
  13. H. L. Royden. Harmonic functions on open Riemann surfaces. Trans. Amer. Math. Soc., 73:40-94, 1952.
  14. G. N. Watson. Three triple integrals. Quarterly J. Math., 10:266- 276, 1939.

Cited by

Sorted by citations

Metadata

Authors
Doyle, P., & Snell, J.
Venue
Carus Mathematical Monographs
Publisher
American Mathematical Society
Published
1984
ISSN
  • 0069-0813
  • 2637-7535
DOI
10.5948/upo9781614440222
Cited by
1,061
References
0
Language
en
Licence
www.cambridge.org/core/terms (unspecified, 10231 d)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review