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30 Apr 2009: First note that a simpleapplication of the CLT (convergence of triangular arrays to the normal law), of (3),(4) and of (16), (20), gives that, if p0 Ct(R) for some ... We recall that the best rate of convergence uniformlyover balls of densities in Ct(R),

30 Apr 2009: function classes of Besov- and Sobolev-type. J. Theor. Probab. 20, 177–199 (2007)16. ... Wiley, New York. (1987)20. Schwartz, L.: Théorie des Distributions. Hermann, Paris (1966)21.

22 Jul 2009: Second, for the lower bound in (d), again using (6), (7) and (20),. ... This proposition, Theorem 1 and the bounds (20) already determine the a.s.

24 Jul 2009: σ20t/2 and variance σ20t implying. E[(. StS0. )p]= ep(p1)σ. 20 t/2. ... In particular, if F0 = BS(σ. 20, ). then Bt(τ, m) = 0 identically.Following Remark 2, it would be interesting to know if there exists continuous martingales,.

24 Jul 2009: Theorem 4.20. Assume that Sτ has a continuous distribution for all τ 0. ... V (k, τ ) = 4 log τ 4 log log τ 4k δ(k, τ ).20.

20 Apr 2009: Date: April 20, 2009. 1. Corollary 3. If F is given by equation (2) and L is hypoelliptic, then F is infinitely differentiable.

9 Aug 2009: See [20]. Acknowledgements. The author acknowledges the contributions of his co-authors Tom Liggett. ... Electronic Jour-nal of Probability, 3, 1–75. Paper #10. [20] Kesten, H., Sidoravicius, V., and Zhang, Y.

2 Jul 2009: Note from (2.16) that. 1. nlog Z(π) ψS (µ) 12λ, (2.20). ... λ. 20 GEOFFREY GRIMMETT AND SVANTE JANSON. 6. Examples. Example 6.1. S = Z0, the Erdős–Rényi random graph.

24 Jun 2009: Claim (3.6) follows fromthis, and the remainder of the proof is to show (3.20). ... Thus (3.20)holds in this case. PHASE TRANSITION OF THE QUANTUM ISING MODEL 17.

8 Jul 2009: We will check that. un , (20). V 2n Vn1Vn1, n 1 (21)and. ... un1. By (20), it suffices to checkthat the two averaging measures are stochastically ordered.