论文信息 - Random walks with badly approximable numbers

Random walks with badly approximable numbers

Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R d give rise to walks with the fastest convergence.

Doug Hensley | Francis Edward Su

[1] Alan Baker,et al. DIOPHANTINE APPROXIMATION (Lecture Notes in Mathematics, 785) , 1981 .

[2] P. Diaconis. Group representations in probability and statistics , 1988 .

[3] F. Su. A LeVeque-type lower bound for discrepancy , 2000 .

[4] U. Porod. The cut-off phenomenon for random reflections , 1996 .

[5] F. Su. Discrepancy Convergence for the Drunkard's Walk on the Sphere , 2001, math/0102205.

[6] Robert F. Tichy,et al. Sequences, Discrepancies and Applications , 1997 .

[7] Lauwerens Kuipers,et al. Uniform distribution of sequences , 1974 .

[9] Simultaneous diophantine approximation , 1972, Bulletin of the Australian Mathematical Society.

[10] J. Rosenthal. Random Rotations: Characters and Random Walks on SO(N) , 1994 .

[11] Alison L Gibbs,et al. On Choosing and Bounding Probability Metrics , 2002, math/0209021.

[12] L. Vulakh. Diophantine approximation in ⁿ , 1995 .

[13] Berry-Esseen bounds and a theorem of Erdös and Turàn on uniform distribution $\mod 1$ , 1973 .