Random walks on finite groups and rapidly mixing Markov chains

David J. Aldous

Séminaire de probabilités de Strasbourg (1983)

  • Volume: 17, page 243-297

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Aldous, David J.. "Random walks on finite groups and rapidly mixing Markov chains." Séminaire de probabilités de Strasbourg 17 (1983): 243-297. <http://eudml.org/doc/113445>.

@article{Aldous1983,
author = {Aldous, David J.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {expository; rapidly mixing Markov chains; hitting time},
language = {eng},
pages = {243-297},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Random walks on finite groups and rapidly mixing Markov chains},
url = {http://eudml.org/doc/113445},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Aldous, David J.
TI - Random walks on finite groups and rapidly mixing Markov chains
JO - Séminaire de probabilités de Strasbourg
PY - 1983
PB - Springer - Lecture Notes in Mathematics
VL - 17
SP - 243
EP - 297
LA - eng
KW - expository; rapidly mixing Markov chains; hitting time
UR - http://eudml.org/doc/113445
ER -

References

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  1. Aldous, D.J. (1982a). Some inequalities for reversible Markov chains. J. London Math. Soc.25564-576. Zbl0489.60077MR657512
  2. Aldous, D.J. (1982b). Markov chains with almost exponential hitting times. Stochastic Processes Appl.13, to appear. Zbl0491.60077MR671039
  3. Aldous, D.J. (1983). On the time taken by a random walk on a finite group to visit every state. Zeitschrift fur Wahrscheinlichkeitstheorie. to appear. Zbl0488.60011MR688644
  4. Diaconis, P. (1982). Group theory in statistics. Preprint. 
  5. Diaconis, P. and Shahshahani, M. (1981). Generating a random permutation with random transpositions. Zeitschrift fur Wahrscheinlichkeitstheorie57159-179. Zbl0485.60006MR626813
  6. Donnelly, K. (1982). The probability that a relationship between two individuals is detectable given complete genetic information. Theoretical Population Biology, to appear. MR700819
  7. Epstein, R.A. (1977). The Theory of Gambling and Statistical Logic (Revised Edition). Academic Press. Zbl0853.90144MR446535
  8. Feller, W. (1968). An Introduction to Probability Theory (3rd Edition). Wiley. Zbl0155.23101MR228020
  9. Gerber, H.U. and Li S.-Y.R. (1981). The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain. Stochastic Processes Appl.11101-108. Zbl0449.60050MR608011
  10. Karlin, S. and Taylor, H.M. (1975). A First Course in Stochastic Processes. Academic Press. Zbl0315.60016MR356197
  11. Keilson, J. (1979). Markov Chain Models--Rarity and Exponentiality. Springer-Verlag. Zbl0411.60068MR528293
  12. Kemeny, J.G. and Snell, J.L. (1959). Finite Markov Chains. Van Nostrand. Zbl0089.13704MR115196
  13. Kemperman, J. (1961). The First Passage Problem for a Stationary Markov Chain. IMS Statistical Research Monograph 1. MR119226
  14. Letac, G. (1981). Problèmes classiques de probabilité sur un couple de Gelfand. Analytical Methods in Probability Theory, ed. D. Duglé et al. SpringerLecture Notes in Mathematics861. Zbl0463.60010MR655266
  15. Li, S.-Y.R. (1980). A martingale approach to the study of occurrence of sequence patterns in repeated experiments. Ann. Probability81171-1176. Zbl0447.60006MR602390
  16. Reeds, J. (1982). Unpublished notes. 
  17. Stout, W.F. (1974). Almost Sure Convergence. Academic Press. Zbl0321.60022MR455094

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