Distributed algorithms with dynamical random transitions

Given any measure-preserving dynamical system (Y, A , , T) and g Lp() , we study convergence of the sequence 1 n n k=1 g TSk , n 1 where Sk is a dynamic Zr -valued random walk generated by another dynamical system, namely an irrational rotation on the d dimensional torus. In this paper, Van der Corput's inequality and number theory are used for studying ergodic theorems and universally representative random sequences. Mathematics subject classification (2000): 60J15, 28D05, 11K36, 11A55. Key words and phrases: Ergodic Theorem, Van der Corput's Inequality, Random Walk, Continued Fractions, Denjoy-Koksma's inequality, Low Discrepancy sequences, Strong Sweeping out property. R E F E R E N C E S [1] BERGELSON, V. Weakly mixing PET. Ergodic Theory Dynam. Systems (1987), Vol 7, No. 3, 337

• Type: Journal
• Year: 2002
• Where: RSA
• Authors: Nadine Guillotin-Plantard, René Schott
• Keywords: Dynamical Systems, Ergodic Theory, RSA 2002, Van Der Corput