11_voichita cleciu. 80KB Jun 04 2011 12:07:25 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 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
In the main Theorem 4.1 we show that regularity of interval matrices can be characterized in terms of determinants (Theorem 4.1, condition (xxxii)), matrix inverses (xxx),
One reason for this is that the Bahadur-Rao theorem, used to get the exponential form of the density in the proof of Theorem 1, takes a different form for lattice laws (see e.g.
One can obtain a new proof of the homogenization result (1.4) from proposition 2.1 by using the fact that Ψ is square integrable on Ω and applying the von Neumann ergodic theorem..
We shall make frequent use of the following inclusion-exclusion type lemma.. The well-known proof is easy, but so short that we include it. It would then follow from Fubini’s
The main step in the proof of Theorem 2.1 is to construct for each bounded C ∞ -domain U containing 0 an auxiliary diffusion with characteristics independent of the environment,
Section 2 has some estimates on the potential kernel for random walks in the plane, while Section 3 has the proof of the stochastic calculus results we need.. Theorem 1.1 in the
