Convergence of random walks on the circle generated by an irrational rotation

DOI10.1090/S0002-9947-98-02152-7zbMath0902.60051MaRDI QIDQ4211121

Francis Edward Su

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

rate of convergencecontinued fractionsdiscrepancyErdős-Turán inequalityrandom walkirrational rotationuniform distribution of sequences

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Continued fractions and generalizations (11J70) Irregularities of distribution, discrepancy (11K38) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Skew products, quantitative recurrence, shrinking targets and decay of correlations ⋮ Dispersion properties of ergodic translations ⋮ Random walks on the circle and Diophantine approximation ⋮ On the Wasserstein distance between classical sequences and the Lebesgue measure ⋮ SMALL AND PSEUDO-SMALL SETS FOR MARKOV CHAINS ⋮ Berry-Esseen bounds and Diophantine approximation ⋮ On the discrepancy of random subsequences of $\{n\alpha\}$ ⋮ On the discrepancy of random subsequences of $\{n\alpha\}$ II ⋮ Diophantine Gaussian excursions and random walks

Uses Software

• Mathematica

Cites Work

• Diophantine approximation
• Comparison techniques for random walk on finite groups
• Random rotations: Characters and random walks on \(SO(N)\)
• The pinwheel tilings of the plane
• The cut-off phenomenon for random reflections
• Berry-Esseen bounds and a theorem of Erdős and Turan on uniform distribution mod 1
• The Grand Tour: A Tool for Viewing Multidimensional Data
• Hecke operators and distributing points on S². II
• On some new questions on the distribution of prime numbers
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