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3 Feb 2013: The ICAmodel PICAd consists of those P Pd with. P(B) =. d. j=1. Pj(wT. j B), Borel B,. for some W W and P1,. ... P(B) =. d. j=1. Pj(wT. j B), Borel B,. for some W W and P1,.

23 Nov 2013: We call wforward extendable if it is an initial segment of some singly infinitedirected SAW from v. ... mapping w to w′. If T is N -subperiodic for some N , we call T subperiodic.

30 Oct 2013: We start by introducing some notation and then give the definition ofthe parabolic Hausdorff dimension. ... Hausdorffdimension. See Billingsley [3] and Cajar [4] for the proof. We first introduce some notation.

28 Oct 2013: For statistical applicationsof the Bernstein–von Mises phenomenon, one typically needs some uniformityin B, and this is where total variation results would be particularly useful. ... sense of Definition 1 holds, and that f0 H s2 for some s > 1/2.

22 May 2013: U1. So p(n)11 = A B(1 α β)n for some A and B.But p. ... i/2)n = (1/2)neinπ/2 = (1/2)n(. cos(nπ/2) i sin(nπ/2)). Thus for some B′ and C′,.

12 Sep 2013: G,ω B), if G contains a path of open edges from some a A to some b B.An open cluster of ω is a maximal set of pairwise-connected ... joining some a A and some b B using only edges thatintersect R.

12 Sep 2013: Throughout, weassume that we have fixed some value of α (0, 1) and d 3. ... every componentcontains points that are within distance nζ from some point of the.

26 Aug 2013: b) If µ(v) = µ for some v V , then µ(v) = µ for all v V. ... Let B = α(2) β as above. Pick p P, andsuppose the fork of branches on p encountered first when descendingfrom the root has size γ for some 1 γ 2.

22 May 2013: Examples of dynamic programming problems and some useful tricks to solve them. ... If Fs1 is the minimum of some collection of linear functions of x1 it follows thatthe same can be said of Fs.

10 Oct 2013: E[XY |G] = Y E[X|G] a.s. Proof. We first consider the case where Y = 1(B), for some B G. ... Proof. Suppose that x converges. Then if for some a < b we had that N([a,b],x) = ,that would imply that lim infn xn a < b lim supn xn, which