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WIAS2013.dvi
https://www.statslab.cam.ac.uk/~rjs57/WIAS2013.pdf3 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,. -
EXTENDABLE SELF-AVOIDING WALKS GEOFFREY R. GRIMMETT, ALEXANDER E.…
https://www.statslab.cam.ac.uk/~grg/papers/ext22.pdf23 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. -
Dimension of Fractional Brownian motion with variable drift Yuval ...
https://www.statslab.cam.ac.uk/~ps422/dim-graph-image.pdf30 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. -
Nonparametric Bernstein-von Mises theorems in Gaussian white noise
https://www.statslab.cam.ac.uk/~nickl/Site/__files/AOS1133.pdf28 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. -
Markov Chains These notes contain material prepared by colleagues ...
https://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf22 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′,. -
Universality for bond percolation in two dimensions
https://www.statslab.cam.ac.uk/~grg/papers/AOP740.pdf12 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. -
Uniformity of the late points of random walk on Znd for d 3
https://www.statslab.cam.ac.uk/~ps422/rwunif2.pdf12 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. -
BOUNDS ON CONNECTIVE CONSTANTSOF REGULAR GRAPHS GEOFFREY R. GRIMMETT…
https://www.statslab.cam.ac.uk/~grg/papers/saw2-final2.pdf26 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. -
Optimization and Control Contents Table of Contents i Schedules ...
https://www.statslab.cam.ac.uk/~rrw1/oc/oc2013.pdf22 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. -
Advanced Probability Perla Sousi∗ December 17, 2011 Contents 1 ...
https://www.statslab.cam.ac.uk/~ps422/notes-2011.pdf10 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 -
Cluster detection in networks using percolation
https://www.statslab.cam.ac.uk/~grg/papers/BEJ412.pdf14 Mar 2013: Proposition 1. Assume that F0 AEP(b, C) for some b > 1 and C > 0. ... Proposition 2. Assume that F0 AEP(b, C) for some b (1, 2) and C > 0. -
Inhomogeneous bond percolation on square, triangular and hexagonal…
https://www.statslab.cam.ac.uk/~grg/papers/AOP729.pdf3 Jul 2013: Some complications arise during transportation,and these may be controlled using probabilistic estimates. ... zero probability. Let k < N , and let k = k(ωk) be the leftmost path in Dk thatreaches some point at height hk. -
Noname manuscript No.(will be inserted by the editor) Bond ...
https://www.statslab.cam.ac.uk/~grg/papers/iso-final6.pdf21 May 2013: Theorem 3.4(Universality). (a) Let π {ρ}{ρ2 j : j 1}. If π exists for some GG , then it isG -invariant.(b) If either ρ or η exists for some ... A horizontal crossingof B = B(M1, M2; N1, N2)is an open path ofB linking some vertexvM1,n1 to some
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