The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Comparison Theorems for Reversible Markov Chains
Open accessAbstract
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp results for the exclusion process.
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Citations
Cites
Biggs, N. (1974) · doi:10.1017/cbo9780511608704 · Cited by 2,940
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Self-citation
Cited by
Information, Physics, and Computation
Mézard, M., & Montanari, A. (2009) · doi:10.1093/acprof:oso/9780198570837.001.0001 · Cited by 1,913
Laplacians and the Cheeger Inequality for Directed Graphs
Chung, F. (2005) · Annals of Combinatorics · doi:10.1007/s00026-005-0237-z · Cited by 535
Exactly Solvable Models for Many-Body Systems Far from Equilibrium
(2001) · Phase Transitions and Critical Phenomena · doi:10.1016/s1062-7901(01)80015-x · Cited by 451
Lectures on finite Markov chains
Saloff-Coste, L. (1997) · Lecture Notes in Mathematics · doi:10.1007/bfb0092621 · Cited by 382
Self-citationRandom Quantum Circuits are Approximate 2-designs
Harrow, A. W., & Low, R. A. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0873-6 · Cited by 324
“nvolves constructing flows, which are weighted sets of paths between states. This can give a tighter bound since bottlenecks are averaged over. This gives a modified comparison theorem: 21 Theorem 4.7 ([12], Theorem 2.3). Let P and Pˆ be two Markov chains on the same state space Ω with the same stationary distribution π…”
BackgroundInfluential
Metadata
- Authors
- Diaconis, P., & Saloff-Coste, L.
- Venue
- The Annals of Applied Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 1993-08-01
- Volume
- 3
- Issue
- 3
- ISSN
- 1050-5164 (ISSN-L)
- OpenAlex
- W1976418263
- Cited by
- 423
- References
- 2
- FWCI
- 8.42
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Diaconis, P., & Saloff-Coste, L. (1993). Comparison Theorems for Reversible Markov Chains. The Annals of Applied Probability. https://doi.org/10.1214/aoap/1177005359
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
