Random walks with badly approximable numbers
نویسندگان
چکیده
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 give rise to walks with the fastest convergence.
منابع مشابه
Badly Approximable Numbers and Vectors in Cantor-like Sets
We show that a large class of Cantor-like sets of Rd, d ≥ 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d ≥ 2. An analogous result is also proved for subsets of Rd arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable...
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