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Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate ...
www.tcm.phy.cam.ac.uk/~gm360/papers/source-free/PhysRevLett.108.256809.pdf24 Jun 2012: Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).[24] G. ... I. Watson, J. Phys. A 24, 4999 (1991).[25] E. Tang, J.-W. -
Correlated Phases of Bosons in the Flat Lowest Band ...
www.tcm.phy.cam.ac.uk/~gm360/papers/source-free/PhysRevLett.108.045306.pdf26 Jan 2012: peripheral sites [24]. In our real gauge, j are. identical up to translation in all unit cells. ... Chern number, in which states cannot be fully localized.[24] The projection to the upper band is similar, as single-. -
Competing Topological Orders in the � ¼ 12=5 Quantum ...
www.tcm.phy.cam.ac.uk/~gm360/papers/source-free/PhysRevLett.108.036806.pdf26 Jan 2012: A similar scan forNe 10 and 12, which was also performed in [24], reveals acharge gap for a 12=5 state with S 2. ... 24] A. Wójs, Phys. Rev. B 80, 041104(R) (2009).[25] Systems on the sphere can exhibit aliasing competition. -
qcmft
www.tcm.phy.cam.ac.uk/~bds10/tp3/secqu.pdf10 Oct 2012: 24 CHAPTER 2. SECOND QUANTISATION. Our aim is to find an operator V̂ in second quantised form whose action on a many-bodystate gives. -
SK2msprnts4.dvi
www.statslab.cam.ac.uk/~yms/SK2msprnts.pdf29 Jun 2012: Cm); they form stochastic submatrices. 10. Page 23, Line 20 and below, and the whole of Page 24 should read asfollows:. ... i}). =1/m 1/(i 1). 1/i(i 1) =i. m. 24. Page 103, Line 13 down:For p = 0, this is trivial, as For p = 0, equality ψp = ψp -
The Bomber Problem Richard Weber† Adams Society of St ...
www.statslab.cam.ac.uk/~rrw1/talks/adams.pdf19 Jan 2012: y(32,3) = arg maxy[0,5.24]. [. c(y)F(31.4 y,2)]. = 14.0079. y(33,3) = arg maxy[0,5.25]. [. ... 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}. -
Research
www.statslab.cam.ac.uk/~rrw1/research.html20 Feb 2012: Incentives for Large Peer-to-Peer Systems, C. Courcoubetis and R. R. Weber, IEEE Journal on Selected Areas in Communications (2006) 24, 1034-1049.> [J. -
Optimization and Control Contents Table of Contents i Schedules ...
www.statslab.cam.ac.uk/~rrw1/oc/oc2012.pdf21 Mar 2012: 24. 6.6 Forward induction policies. 24. 7 Average-cost Programming 25. 7.1 Average-cost optimality equation. -
Lund.dvi
www.statslab.cam.ac.uk/~rjs57/Lund.pdf13 Sep 2012: K}. We aim to minimise the misclassification error rate orrisk :. Risk(C) = P(. C(X) 6= Y). September 13, 2012- 24. R. -
Optimal weighted nearest neighbourclassifiers Richard…
www.statslab.cam.ac.uk/~rjs57/Essex.pdf21 Sep 2012: Γ(. 2 2d)2d/(d4). 24/(d4). R. J. Samworth Nonparametric classification. Further regret comparisons. -
gc001085 1..24
www.statslab.cam.ac.uk/~rjs57/2005GC001085.pdf10 Nov 2012: ISSN: 1525-2027. Copyright 2006 by the American Geophysical Union 1 of 24. ... GeochemistryGeophysicsGeosystems G3G3 poore et al.: neogene overflow of ncw 10.1029/2005GC001085. 4 of 24. -
rssb_1034 ..
www.statslab.cam.ac.uk/~rds37/papers/Shah%20Samworth%202013%20Variable%20selection%20with%20error%20control%20-%20another%20look%20at%20stability%20selection.pdf20 Dec 2012: 104 5:12 104 1:32 103 2:59 103 4:37 1030.54 1:01 104 4:81 104 1:24 103 2:44 103 4:13 1030.55 ... 02 105 1:46 104 2:33 1040.88 7:64 106 3:12 105 7:24 105 1:32 104 2:11 1040.89 6:85 106 2:80 105 -
Mobile Geometric Graphs: Detection, Coverage and Percolation Yuval…
www.statslab.cam.ac.uk/~ps422/tperc.pdf20 Apr 2012: E [vol (Wg(t))] c E [vol (W0(t))]. (7). The expected volume of the Wiener sausage with g 0 is known to satisfy [24, 2]. ... P [Kct ] t exp(c1L). (24). We will now derive an upper bound for P[H̃t]. -
The Isolation Time of Poisson Brownian Motions Yuval Peres∗ ...
www.statslab.cam.ac.uk/~ps422/isolation.pdf14 Mar 2012: P (Tisol > t) = exp. (c̃d. t. Ψd(t)(1 o(1)). )? (24). Peres et al. [14] and Peres and Sousi [15] studied the detection time for the case when u also ... ClearlyTnonperc Tisol. We conclude with the question below. Question. Do the tail probabilities of -
Collisions of Random Walks Martin T. Barlow∗ Yuval Peres† ...
www.statslab.cam.ac.uk/~ps422/collisions-rws.pdf20 Apr 2012: 24. (5.19). Hence the number of rounds before hitting the root has a Geometric distribution,so it has bounded expectation. ... 1. α2β(n1)1lk=2. Po(Zn, > 0,Zn,k > 0). (5.24). 25. We let An, = Jn,1 Jn, Jn,1, for = 1, ,α2β(n1) 1 and for = 0 we -
Probab. Theory Relat. FieldsDOI 10.1007/s00440-012-0446-z Adaptive…
www.statslab.cam.ac.uk/~nickl/Site/__files/ptrf13.pdf3 Sep 2012: 6)) and since gn (t, B),. ‖ VJn ( f gn)‖22 infg ‖ f g‖22 c(B)22 Jn t 4τn (24). ... the inequality holding for L 0 large enough and some c > 0, as in (24). -
Probab. Theory Relat. Fields (2012) 153:363–404DOI…
www.statslab.cam.ac.uk/~nickl/Site/__files/ptrf12.pdf1 Jun 2012: 24]. On Sd the differential operator L coincideswith the usual Laplace–Beltrami operator, and we have. ... As mentioned in (24) abovethis is tantamount to assuming a classical t -Hölder condition on f. -
Rates of contraction for posterior distributions in Lr-metrics, 1
www.statslab.cam.ac.uk/~nickl/Site/__files/AOS924.pdf6 Mar 2012: r. Lr. 2j n.(24). If r = , for p0 and bounded, there exists a constant L such that for all jsatisfying 2j j < n we have. ... PROOF. Since Bα = W2α in [24] and it also equals a constant times Rα in [32],this proposition simply combines Theorem 2.1 in -
On adaptive inference and confidence bands
www.statslab.cam.ac.uk/~nickl/Site/__files/AOS903.pdf10 Jan 2012: Following Li [24] the bandCn is called asymptotically honest with level α for a family of probability densitiesP if it satisfies the asymptotic coverage inequality. -
vanzwet.dvi
www.statslab.cam.ac.uk/~grg/papers/USvanzwet.pdf15 Aug 2012: Mathematics and its Applications, vol. 99, Springer, New York, pp. 1–24.Aizenman, M. -
notes.dvi
www.statslab.cam.ac.uk/~grg/papers/USstflour.pdf15 Aug 2012: PERCOLATION ANDDISORDERED SYSTEMS. Georey GRIMMETT. 2PREFACEThis course aims to be a (nearly) self-contained account of part of the mathematicaltheory of percolation and related topics. The rst nine chapters summarise rigorousresults in percolation -
notes.dvi
www.statslab.cam.ac.uk/~grg/papers/USrednotes.pdf15 Aug 2012: PERCOLATION ANDDISORDERED SYSTEMSGeorey GRIMMETT. 2PREFACEThis course aims to be a (nearly) self-contained account of part of the mathematicaltheory of percolation and related topics. The rst nine chapters summarise rigorousresults in percolation -
rctree.dvi
www.statslab.cam.ac.uk/~grg/papers/USrctree.pdf15 Aug 2012: BRANCHING PROCESSES, AND. RANDOM-CLUSTER MEASURES ON TREES. Geoffrey Grimmett, Svante JansonAbstra t. Random-cluster measures on infinite regular trees are studied in con-junction with a general type of ‘boundary condition’, namely an -
rcproc.dvi
www.statslab.cam.ac.uk/~grg/papers/USrcproc.pdf15 Aug 2012: φbp,q = αφ′ (1 α)φ′′. for some distinct φ′,φ′′ Rp,q. It follows by [24, Thm. ... The given statement for θ0 may be proved similarly, making use of Theorem3.2 and [24, Prop. -
potts2.dvi
www.statslab.cam.ac.uk/~grg/papers/USpotts2.pdf15 Aug 2012: POTTS MODELS AND RANDOM-CLUSTER. PROCESSES WITH MANY-BODY INTERACTIONS. Geoffrey GrimmettAbstra t. Known differential inequalities for certain ferromagnetic Potts models with pair-interactions may be extended to Potts models with many-body -
pinball.dvi
www.statslab.cam.ac.uk/~grg/papers/USpinball.pdf15 Aug 2012: Rotator pin-ball. Ruijgrok and Cohen [24] have proposed a general studyof mirror and rotator' models. ... Quas, A., Some properties of Lorentz lattice gas models (1996) (to appear).24. -
opt.dvi
www.statslab.cam.ac.uk/~grg/papers/USopt.pdf15 Aug 2012: See [24, 51, 52] for more informa-tion and references.Few non-trivial facts are known about the limit set L, and much eort hasbeen spent, largely inconclusively, on attempting to -
meanf.dvi
www.statslab.cam.ac.uk/~grg/papers/USmeanf.pdf15 Aug 2012: THE RANDOM-CLUSTER MODEL. ON THE COMPLETE GRAPH. Béla Bollobás, Geoffrey Grimmett, Svante JansonAbstract. The random-cluster model of Fortuin and Kasteleyn contains as specialcases the percolation, Ising, and Potts models of statistical physics. -
mcst.dvi
www.statslab.cam.ac.uk/~grg/papers/USmcst.pdf15 Aug 2012: 24 C. BEZUIDENHOUT, G. GRIMMETT, A. LOFFLERwhence, by Wald's equation ([13], p. -
keane.dvi
www.statslab.cam.ac.uk/~grg/papers/USkeane.pdf15 Aug 2012: Theorem 6. [24] We have that µp(K = 1) = 1 whenever p > pentc. ... Soc., 130:175–188, 2001. MR1797779. [24] O. Häggström. Uniqueness of the infinite entangled component in three-dimensional bond percolation. -
inter4.dvi
www.statslab.cam.ac.uk/~grg/papers/USinter4.pdf15 Aug 2012: Using (5.17)–(5.18) of[22], together with estimates at the beginning of the proof of Lemma (2.24) of [29],we find that. ... We have forf W(δ1) QG/3(e1) that. τ[QG/3(f) EL1,M1. ]= QG/3(τf) EL2,M2, (24). -
entperc.dvi
www.statslab.cam.ac.uk/~grg/papers/USentperc.pdf15 Aug 2012: Et(ΨA) aΛs(A) b. for every increasing cylinder event A. Here are some remarks about these two lemmas, which are essentially equa-tions (13.24) and (13.25) of [7]. -
ems.dvi
www.statslab.cam.ac.uk/~grg/papers/usems.pdf15 Aug 2012: THE RANDOM-CLUSTER MODEL. Geoffrey GrimmettAbstra t. The class of random-cluster models is a unification of a variety of sto-chastic processes of significance for probability and statistical physics, including per-colation, Ising, and Potts models; -
elec.dvi
www.statslab.cam.ac.uk/~grg/papers/USelec.pdf15 Aug 2012: 2.24) x = f (x). As is well known (see Harris (1963) proof of Theorem I.6.1) the only solutions of(2.24) in [0, 1] are q and 1. ... 24 GEOFFREY GRIMMETT AND HARRY KESTEN. as n. Proof. We prove. -
decay2.dvi
www.statslab.cam.ac.uk/~grg/papers/USdecay2.pdf15 Aug 2012: Whenq = 2, this role is played by the Simon{Lieb inequality (see [24, 27]). ... 1986). Phase coexistence and surface tensions for the Pottsmodel. Communications in Mathematical Physics 105, 527{545.24. -
crit6.dvi
www.statslab.cam.ac.uk/~grg/papers/UScrit6.pdf15 Aug 2012: CRITICAL PROBABILITIES FOR SITE. AND BOND PERCOLATION MODELS. G. R. Grimmett and A. M. Stacey. Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeAbstract. Any infinite graph G = (V, E) has a site percolation critical -
bg6.dvi
www.statslab.cam.ac.uk/~grg/papers/USbg6.pdf15 Aug 2012: Our basic strategy in proving the central limit theorem isto adapt the arguments proposed by Kipnis and Varadhan [24] and further developed byDeMasi, Ferrari, Goldstein, and Wick [10, 11]. ... One of the main properties of the chain Xω is its -
PERCOLATION SINCE SAINT-FLOUR GEOFFREY R. GRIMMETT AND HARRY KESTEN…
www.statslab.cam.ac.uk/~grg/papers/stf.pdf2 Jul 2012: Probab. 24 (1996), 1036–1048. 4. M. Atapour and N. Madras, On the number of entangled clusters, J.Statist. ... J. Probab. Stat. 24 (2010), 300–320. 114. H. Kesten, V. Sidoravicius, and Y. -
sjqrw3.dvi
www.statslab.cam.ac.uk/~grg/papers/sjqrw3.pdf15 Aug 2012: min h, max h] =. [. 12,. 12. ]. (24). For a general unbiased walk, we take ascoin flip the unitary matrix. ... We have as beforethat the domain of the limit distribution is asin (24). -
rol.dvi
www.statslab.cam.ac.uk/~grg/papers/rol.pdf15 Aug 2012: F., Percolation theory and some. applications, Itogi Nauki i Techniki (Series of Probability Theory, Mathematical Statistics,Theoretical Cybernetics) 24 (1986), 53–110. -
pw.dvi
www.statslab.cam.ac.uk/~grg/papers/pw.pdf15 Aug 2012: mains unproved. Using Theorem 4.2 and an argument of Zhang (see [24, p. ... Related Fields 92, 511–527. 24. Grimmett, G. R. (1989), Percolation, Springer–Verlag, Berlin. -
Three theorems in discrete random geometry
www.statslab.cam.ac.uk/~grg/papers/PS_2011_185-rev.pdf27 Jan 2012: gular and hexagonal lattices, [24],(c) the critical point of the random-cluster model on the square lattice with. ... 6See also [51]. Three theorems in discrete random geometry 315. Theorem 3.4 ([24]). -
orient2.dvi
www.statslab.cam.ac.uk/~grg/papers/orient2.pdf15 Aug 2012: Directed percolation is closely related to the contact model, for which blockarguments have been used to prove results related to some of those describedabove (see [7, 12, 23, 24]). -
notes-reprint2012.dvi
www.statslab.cam.ac.uk/~grg/papers/notes-reprint2012.pdf15 Aug 2012: PERCOLATION AND. DISORDERED SYSTEMS. Geoffrey GRIMMETT. Percolation and Disordered Systems 143. PREFACE. This course aims to be a (nearly) self-contained account of part of the math-ematical theory of percolation and related topics. The first nine -
Influence and sharp-threshold theorems for monotonic measures
www.statslab.cam.ac.uk/~grg/papers/influe.pdf15 Aug 2012: 2.24) λ(C | Uj = 1) = λ(g(U ) A) λ(f (U ) A) = λ(B | Uj = 1). -
houches.dvi
www.statslab.cam.ac.uk/~grg/papers/houches.pdf15 Aug 2012: θΛ(p, q) = φΛ,p,q(A). (24). It is not hard to see that. -
dwgrim.dvi
www.statslab.cam.ac.uk/~grg/papers/dwgrim.pdf15 Aug 2012: the links between the Potts partition functionand the Tutte polynomial surveyed earlier by Welsh and Merino, [24]. ... 24] D. J. A. Welsh and C. Merino. The Potts model and the Tutte polyno-mial. -
grimmett.dvi
www.statslab.cam.ac.uk/~grg/papers/camnato.pdf15 Aug 2012: 24] for a discussion). If d 3 and q is sufficiently large, then the uniqueness is aconsequence of Pirogov–Sinai theory ([37, 39]). ... 1992). Potts models and random-cluster processes with many-body interac-. tions (to appear).24. -
Random-cluster representation of the Blume–Capel model B. T. Graham,…
www.statslab.cam.ac.uk/~grg/papers/blume.pdf15 Aug 2012: limΛLd. φ0Λ(A B) = Φ0(1A(ψ)µ0ψ(B)). (7.7). 24 B. T. Graham and G. -
Geometry of Lipschitz percolation
www.statslab.cam.ac.uk/~grg/papers/AIHP403.pdf11 Apr 2012: Ax,m(n)) nnr=0 hmp (r). 1. (24). Once this is proved, it follows by (23) that. ... prove (24), and the proof is essentially that of [11], Lemma 5.17.
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