Abstract
AbstractGiven n vectors {i} ∈ [0, 1)d, consider a random walk on the d‐dimensional torus 𝕋d = ℝd/ℤd generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*k) ≥ C1k−n/2, where C1 = C(n, d) is a constant. If the vectors are badly approximated by rationals (in a sense we will define), then D(Q*k) ≤ C2k−n/2d for C2 = C(n, d, j) a constant. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
