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A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
2011/1/21
We provide conditions which yield a strong law of large num-bers for expressions of the form 1/N PN n=1 FX(q1(n)), · · · ,X(qℓ(n)) where X(n), n 0’s is a sufficiently fast mixing ve...
Let A {1, . . . ,N} and P1, . . . , Pℓ 2 Z[n] with Pi(0) = 0 and deg Pi = k for every 1 i ℓ.We show, using Fourier analytic techniques, that for every ε > 0, there necessarily exists...