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A nilpotent IP polynomial multiple recurrence theorem
ergodic Ramsey theory IP-sets nilpotent Hales-Jewett theorem nilpotent Szemeredi theorem
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2012/6/14
We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibm...
A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
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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...