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  2. 8 Apr 2017: We created 25 artificial signals at each sparsity levels {1, 4, 10, 20, 35, 54}. ... 1.0. Sparsity. Pow. er. 0.4. 0.6. 0.8. 1.0. 1 4 10 20 35 54.
  3. Strong law of large numbers for the capacity of ...

    www.statslab.cam.ac.uk/~ps422/wiener7.pdf
    22 Dec 2017: 20. Proof of Lemma 3.8. We first extend the definition of the τi and Ai to negative indices:. ... C. (n exp(λ. L) exp. (c ε. 2n. E[Y 20]. Lε. )).
  4. Mixing time for random walk on supercritical dynamical percolation ...

    www.statslab.cam.ac.uk/~ps422/supercritical-draft.pdf
    15 Aug 2017: 20. Proof. Since τδ is a stopping time, it follows that {τδ t(n) > τi}Fτi, and hence we obtain. ... Êx,η[Zτk1(τδ t(n) > τk)] 1. n10d,. and hence, since N = (log n)γ n2 with γ = 8d 20 > 2β 1, we deduce.
  5. 17 Mar 2017: 2.1 Class structure. 20. 2.2 Hitting times. 21. 2.3 Recurrence and transience. ... Remark 2.20. Note that in the above theorem we required X to be recurrent in order to provethat the equivalence holds.
  6. Convergence of the SAW on random quadrangulations to SLE8/3 on…

    www.statslab.cam.ac.uk/~jpm205/slides/saw_convergence_paris_january_2017.pdf
    22 Jan 2017: Jason Miller (Cambridge) Convergence of the SAW on ’s to SLE(8/3) January 24, 2017 20 / 26. ... Q+. Qzip. Q. Jason Miller (Cambridge) Convergence of the SAW on ’s to SLE(8/3) January 24, 2017 20 / 26.
  7. Convergence of percolation on random quadrangulations

    www.statslab.cam.ac.uk/~jpm205/slides/percolation_convergence_oxford_may_2017.pdf
    1 Jun 2017: Simulations due to Tom Kennedy.Jason Miller (Cambridge) Convergence of percolation on random s May 22, 2017 20 / 28.
  8. NEW FRONTIERS IN RANDOM GEOMETRY (RaG)EP/I03372X/1 REPORT 1/7/16 – ...

    www.statslab.cam.ac.uk/~grg/rag-reports/report2017.pdf
    23 Oct 2017: 20. Random walks on the random graph, Nathanael Berestycki, EyalLubetzky, Yuval Peres, Allan Sly, Annals of Probability. ... Grimmett, Z.Li, European Journal of Combinatorics 20 (2013), Paper P47, 14 pp.
  9. Connective constants and height functions for Cayley graphs

    www.statslab.cam.ac.uk/~grg/papers/tran7166.pdf
    18 Aug 2017: The Higman group Γ of [20] is an infinite, finitely presented groupwith presentation Γ = 〈S | R〉 where.
  10. 25 Sep 2017: Date: 20 September 2017.2010 Mathematics Subject Classification. 91B12. 1. 2 GRIMMETT ET AL.
  11. SELF-AVOIDING WALKS AND AMENABILITY GEOFFREY R. GRIMMETT AND…

    www.statslab.cam.ac.uk/~grg/papers/new10.pdf
    3 Jul 2017: In summary,. {e1,e2} ={〈1,s1t 〉,〈1,st〉. }, {g1,g2} =. {〈1,s1t2〉,〈1,st2〉. }. 20 GEOFFREY R. ... Amer. Math. Soc. 369 (2017), 5961–5980.[20] , Self-avoiding walks and connective constants, (2017), http://arxiv.org/abs/1704.

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