PERCOLATION AND DISORDERED SYSTEMS Geoffrey GRIMMETT

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300 <strong>Geoffrey</strong> Grimmett 323. Roy, R. and Meester, R. (1996). Continuum Percolation. Cambridge University Press, Cambridge. 324. Ruijgrok, T. W. and Cohen, E. G. D. (1988). Deterministic lattice gas models. Physics Letters A 133, 415–418. 325. Russo, L. (1978). A note on percolation. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 43, 39–48. 326. Russo, L. (1981). On the critical percolation probabilities. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 56, 229–238. 327. Russo, L. (1982). An approximate zero-one law. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 129–139. 328. Scheinerman, E. R. and Wierman, J. C. (1987). Infinite AB percolation clusters exist. Journal of Physics A: Mathematical and General 20, 1305–1307. 329. Schonmann, R. H. (1994). Theorems and conjectures on the dropletdriven relaxation of stochastic Ising models. Probability and Phase Transition (G. R. Grimmett, ed.), Kluwer, Dordrecht, pp. 265–310. 330. Seymour, P. D. and Welsh, D. J. A. (1978). Percolation probabilities on the square lattice. Advances in Graph Theory (B. Bollobás, ed.), Annals of Discrete Mathematics 3, North-Holland, Amsterdam, pp. 227–245. 331. Simon, B. (1980). Correlation inequalities and the decay of correlations in ferromagnets. Communications in Mathematical Physics 77, 111–126. 332. Sinai, Ya. G. (1982). Theory of Phase Transitions: Rigorous Results. Pergamon Press, Oxford. 333. Slade, G. (1991). The lace expansion and the upper critical dimension for percolation. Mathematics of Random Media (W. E. Kohler and B. S. White, eds.), Lectures in Applied Mathematics, vol. 27, American Mathematical Society, Providence, pp. 53–63. 334. Slade, G. (1995). Bounds on the self-avoiding walk connective constant, Special Issue: Proceedings of the Conference in Honor of Jean-Pierre Kahane, 1993. Journal of Fourier Analysis and its Applications, 525–533. 335. Stacey, A. M. (1996). The existence of an intermediate phase for the contact process on trees. Annals of Probability 24, 1711–1726. 336. Stauffer, D. (1981). Scaling properties of percolation clusters. Disordered Systems and Localization (C. Castellani, C. DiCastro, and L. Peliti, eds.), Springer, Berlin, pp. 9–25. 337. Swendsen, R. H. and Wang, J. S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Physical Review Letters 58, 86– 88. 338. Sykes, M. F. and Essam, J. W. (1964). Exact critical percolation probabilities for site and bond problems in two dimensions. Journal of Mathematical Physics 5, 1117–1127.
Percolation and Disordered Systems 301 339. Tanemura, H. (1996). Critical behavior for a continuum percolation model. Probability Theory and Mathematical Statistics (Tokyo 1995), World Scientific, pp. 485–495. 340. Vahidi-Asl, M. Q. and Wierman, J. C. (1990). First-passage percolation on the Voronoi tesselation and Delaunay triangulation. Random Graphs ’87, Wiley, London, pp. 341–359. 341. Vahidi-Asl, M. Q. and Wierman, J. C. (1990). A shape result for first-passage percolation on the Voronoi tesselation and Delaunay triangulation. Random Graphs ’89, Wiley, London, pp. 247–262. 342. Vahidi-Asl, M. Q. and Wierman, J. C. (1993). Upper and lower bounds for the route length of first-passage percolation in Voronoi tesselations. Bulletin of the Iranian Mathematical Society 19, 15-28. 343. Wang, F. and Cohen, E. G. D. (1995). Diffusion in Lorentz lattice gas cellular automata: the honeycomb and quasi-lattices compared with the square and triangular lattices. Journal of Statistical Physics 81, 467–495. 344. Watts, G. M. T. (1996). A crossing probability for critical percolation in two dimensions. Journal of Physics A: Mathematical and General 29, L363–L368. 345. Welsh, D. J. A. (1993). Percolation in the random-cluster process. Journal of Physics A: Mathematical and General 26, 2471–2483. 346. Whittle, P. (1986). Systems in Stochastic Equilibrium. John Wiley, Chichester. 347. Whittle, P. (1994). Polymer models and generalised Potts–Kasteleyn models. Journal of Statistical Physics 75, 1063–1092. 348. Wierman, J. C. (1987). Directed site percolation and dual filling models. Annals of Discrete Mathematics 33, 339–352. 349. Wierman, J. C. (1987). Duality for k-degree percolation on the square lattice. Percolation Theory and Ergodic Theory of Infinite Particle Systems (H. Kesten, ed.), Springer, Berlin, pp. 311–323. 350. Wierman, J. C. (1988). Bond percolation critical probability bounds derived by edge contraction. Journal of Physics A: Mathematical and General 21, 1487–1492. 351. Wierman, J. C. (1988). AB percolation on close-packed graphs. Journal of Physics A: Mathematical and General 21, 1939–1944. 352. Wierman, J. C. (1988). On AB percolation in bipartite graphs. Journal of Physics A: Mathematical and General 21, 1945–1949. 353. Wierman, J. C. (1989). AB percolation: a brief survey. Combinatorics and Graph Theory, vol. 25, Banach Centre Publications, Warsaw, pp. 241–251. 354. Wierman, J. C. (1990). Bond percolation critical probability bounds for the Kagomé lattice by a substitution method. Disorder in Physical Systems (G. R. Grimmett and D. J. A. Welsh, eds.), Clarendon Press, Oxford, pp. 349–360.
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PERCOLATION AND DISORDERED SYSTEMS
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144 Geoffrey Grimmett ÈÊÇ��
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146 Geoffrey Grimmett 8. Critical P
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148 Geoffrey Grimmett θ(p) 1 pc 1
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150 Geoffrey Grimmett physical imag
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152 Geoffrey Grimmett Fig. 2.1. Par
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154 Geoffrey Grimmett Fig. 2.2. An
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156 Geoffrey Grimmett 3.1 Percolati
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158 Geoffrey Grimmett Kesten [201]
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160 Geoffrey Grimmett whence d dp P
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Page 24 and 25:
164 Geoffrey Grimmett s 1 θ = 0 pc
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166 Geoffrey Grimmett ∂B(n) 0 e f
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168 Geoffrey Grimmett Fig. 4.5. A s
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170 Geoffrey Grimmett Theorem 5.5 (
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172 Geoffrey Grimmett Proof of Theo
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174 Geoffrey Grimmett 5.3 Site and
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176 Geoffrey Grimmett 6.1 Using Sub
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178 Geoffrey Grimmett Now φ(p) = 0
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180 Geoffrey Grimmett so that (3.10
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182 Geoffrey Grimmett x 2 y 2 x 4 x
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184 Geoffrey Grimmett Similarly, Pp
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186 Geoffrey Grimmett It remains to
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188 Geoffrey Grimmett Fix β < pc a
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190 Geoffrey Grimmett where δ 2 =
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192 Geoffrey Grimmett Fig. 7.1. Tak
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196 Geoffrey Grimmett 4. The open c
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198 Geoffrey Grimmett For n > m, le
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200 Geoffrey Grimmett Lemma 7.17. I
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202 Geoffrey Grimmett Lemma 7.24. S
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204 Geoffrey Grimmett 000 111 000 1
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208 Geoffrey Grimmett Fig. 7.9. The
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210 Geoffrey Grimmett Fig. 7.10. Il
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214 Geoffrey Grimmett may be shown
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216 Geoffrey Grimmett Lemma 8.11. L
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218 Geoffrey Grimmett 0 u noting th
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220 Geoffrey Grimmett where α ′
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222 Geoffrey Grimmett The infra-red
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224 Geoffrey Grimmett 9. PERCOLATIO
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226 Geoffrey Grimmett Fig. 9.2. If
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228 Geoffrey Grimmett x Fig. 9.3. I
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230 Geoffrey Grimmett for crossing
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232 Geoffrey Grimmett 10. RANDOM WA
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234 Geoffrey Grimmett the volume of
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236 Geoffrey Grimmett We define sim
Page 98 and 99:
238 Geoffrey Grimmett We now use th
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240 Geoffrey Grimmett p+ 1 pc(site)
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242 Geoffrey Grimmett Fig. 10.6. Th
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244 Geoffrey Grimmett Fig. 10.7. Th
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246 Geoffrey Grimmett A L d -path i
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248 Geoffrey Grimmett where pc(site
Page 110 and 111: 250 Geoffrey Grimmett now make two
Page 112 and 113: 252 Geoffrey Grimmett Fig. 11.1. Th
Page 114 and 115: 254 Geoffrey Grimmett Fig. 11.2. Th
Page 116 and 117: 256 Geoffrey Grimmett II. P(C �=
Page 118 and 119: 258 Geoffrey Grimmett Theorem 11.13
Page 120 and 121: 260 Geoffrey Grimmett (b) Under wha
Page 122 and 123: 262 Geoffrey Grimmett is obtained b
Page 124 and 125: 264 Geoffrey Grimmett 13.2 Weak Lim
Page 126 and 127: 266 Geoffrey Grimmett where p = 1
Page 128 and 129: 268 Geoffrey Grimmett Evidently pg(
Page 130 and 131: 270 Geoffrey Grimmett That is to sa
Page 132 and 133: 272 Geoffrey Grimmett which, via Le
Page 134 and 135: 274 Geoffrey Grimmett Turning to th
Page 136 and 137: 276 Geoffrey Grimmett Each circuit
Page 138 and 139: 278 Geoffrey Grimmett If A(q) < 1 (
Page 140 and 141: 280 Geoffrey Grimmett REFERENCES 1.
Page 142 and 143: 282 Geoffrey Grimmett 30. Alexander
Page 144 and 145: 284 Geoffrey Grimmett 63. Berg, J.
Page 146 and 147: 286 Geoffrey Grimmett 93. Chayes, J
Page 148 and 149: 288 Geoffrey Grimmett 123. Durrett,
Page 150 and 151: 290 Geoffrey Grimmett 158. Grimmett
Page 152 and 153: 292 Geoffrey Grimmett 191. Higuchi,
Page 154 and 155: 294 Geoffrey Grimmett 224. Koteck´
Page 156 and 157: 296 Geoffrey Grimmett 259. Meester,
Page 158 and 159: 298 Geoffrey Grimmett 290. Newman,
Page 162 and 163: 302 Geoffrey Grimmett 355. Wierman,
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