Year: 2004
Type: article
Abstract: Given 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
Source: Random Structures and Algorithms
DOI: 10.1002/rsa.20029
Authors: Timothy Prescott, Francis Edward Su
Institutions: University of California, Los Angeles, Harvey Mudd College
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2135570362