article03_6. 317KB Jun 04 2011 12:06:51 AM
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The following theorem is the indefinite version of the Chaotic Furuta inequality, a result previously stated in the context of Hilbert spaces by Fujii, Furuta and Kamei [ 5 ]..
The deepest input will be Lemma 2.1 be- low which only requires pre-Prime Number Theorem elementary methods for its proof (in Tenenbaum’s [11] introductory book on analytic
Similarly to the above sketched argument for Pourchet’s Theorem, the conclusions about the continued fraction will be derived from a “Thue-type” inequality for the
The proof of this theorem relies on a result of Razon about fields which are PAC over subfields, on Frobenius density theorem, and on Neukirch’s recognition of p -adically closed
The proof serves to demonstrate two innovations: a strong re- pulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem
tridiagonal matrices, we now give a further proof of this fact based on Theorem 1.3 and in the spirit of the divide and conquer algorithm due to Sorensen and Tang [9], but see also
Lemma 2.2 follows from [11, Theorem 1] (or see [12, Theorem 3.1]), in which the problem of classifying systems of forms and linear mappings over a field of characteristic not 2
We now show how the uniform law of large numbers in Theorem 1.1 can be used to prove the hydrodynamic limits for the system of RWRE as stated in Theorem 1.4.. Proof of Theorem 1.4:
