Rates of convergence of random walk on distance regular graphs

Probability Theory and Related Fields

Volumn 112, Issue 4, 1998, Pages 493-533

  Belsley, Eric David ^a  

^a Department of Biology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032285370     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050198     Document Type: Article

References (27)

1. Aldous, D., Diaconis, P.: Shuffling Cards and Stopping Times. Amer. Math. Monthly 93, 333-348 (1986)
2. Aldous, D., Diaconis, P.: Strong uniform times and finite random walks. Adv. App. Math. 8, 69-97 (1987)
3. Artin, E.: Geometric Algebra. Interscience Publishers, New York, N.Y. (1966)
4. Atkinson, F.: Discrete and Continuous Boundary Problems. Academic Press, New York, N.Y. (1964)
5. Bannai, E., Ito, T.: Algebraic Combinatorics I: Association Schemes. Benjamin, Menlo Park, CA. (1984)
6. Bannai, E., Ito, T.: Current researches on algebraic combinatories. Graphs Combin. 2, 287-308 (1986)
7. Belsley, E.: Rates of convergence of Markov chains related to Association Schemes. PhD thesis, Dept. of Math., Harvard University. (1993)
8. Bhattacharya, R., Waymire, E.: Stochastic Processes with Applications. Wiley, New York, N.Y. (1990)
9. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer-Verlag, New York, N.Y. (1989)
10. Carter, R.: Simple Groups of Lie Type. Wiley, New York, N.Y. (1972)
11. D'Aristotle, A.: The nearest neighbor random walk on subspaces of a vector space and rate of convergence. Jour. Th. Prob. 8, 321-346 (1993)
12. Diaconis, P.: Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward, CA. (1986)
13. Diaconis, P.: The cutoff phenomenon in finite Markov chains. Preprint, Math Dept., Harvard University, Cambridge. (1996)
14. Diaconis, P., Fill, J.: Strong stationary times via a new form of duality. Ann. Prob. 18, 1483-1522 (1990)
15. Diaconis, P., Saloff-Coste, L.: Moderate growth and random walk on finite groups. Geom. and Func. Anal. 4, 1-36 (1994)
16. Diaconis, P., Saloff-Coste, L.: Random walks on finite groups: a survey of analytic techniques. In: Probability Measures on Groups and Related Structures. World Scientific. (1995)
17. Diaconis, P., Shahshahani, M.: Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Geb. 57, 159-179 (1981)
18. Diaconis, P., Shahshahani, M.: Time to reach stationarity in the Bernoulli-Laplace diffusion model. SIAM J. Math. Anal. 18, 208-218 (1987)
19. Diaconis, P., Stroock, D.: Geometric bounds for eigenvalues of Markov chains. Ann. App. Prob, 1, 36-61 (1991)
20. Fill, J.A.: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. Ann. App. Prob, 1, 62-87 (1991)
21. Gasper, G., Rahman, M.: Basic Hypergeometric Series. Cambridge University Press, Cambridge, UK. (1990)
22. Greenhalgh, A.: Measures on Groups with Subgroup Invariance Properties. PhD thesis, Stanford University. (1989)
23. q) by random transvections. Jour. of Alg. Comb. 1, 133-150 (1992)
24. Hora, A.: Critical Phenomena for Plandorn Walks on P- and Q-polynomial association schemes. Preprint, Dept. of Environmental and Mathematical Sciences, Okayama University, Japan. (1996)
25. Kemperman, J.: The Passage Problem for a Stationary Markov Chain. U. of Chicago Press, Chicago, IL. (1961)
26. Leonard, D.: Orthogonal polynomials, duality and Association Schemes. Siam. J. Math. Anal. 13, 656-663 (1982)
27. MacWilliams, J., Sloane, W.: The Theory of Error Correcting Codes. North-Holland, Amsterdam. (1977)