Not to be fed after midnight. 3 0 obj Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Material based on Grimmett's probability on graphs book and the book by Bollobás and Riordan. Material based on Grimmett's percolation book and discussions with Gady Kozma. March 12'th in class. Material based on Grimmett's percolation book and discussions with Gady Kozma. Survey of some related topics not treated in our course: Percolation on Cayley graphs of groups, percolation on finite graphs (e.g., the hypercube or the complete graph), long-range percolation on Z, the triangle condition and its uses in high-dimensional percolation, the random cluster model. Application of the BK inequality show that the mean cluster size at p_c is infinite. Lecture 4 (19.3): Description of general FKG inequality. (Why assign movies and film clips? Lecture 9 (21.5 - only two hours): Cardy's formula and its history. Lecture 7 (30.4): Exponential decay of tail of cluster size. Supercritical phase: uniqueness of the infinite cluster. Supercritical phase: uniqueness of the infinite cluster. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. The exercise needs to be handed in by Proof of statements for large enough p. Definition of slab critical point. Introduction to conformal invariance. Material based on Grimmett's percolation book. Exercise 2. ( Log Out / ( Log Out / Material based on Grimmett's percolation book and discussions with Gady Kozma. << Material based on Grimmett's percolation book. The Liggett-Schonmann-Stacey theorem on domination of a dependent percolation by an independent one. Use of it to start proving the statements for p>p_c. Application of the BK inequality show that the mean cluster size at p_c is infinite. Statement and proof of the Van den Berg-Kesten inequality. Lecture 5 (9.4): Comparison of p_c for the square and triangular lattices using the Aizenman-Grimmett method. Proof of statements for large enough p. Definition of slab critical point. Lecture 5 (9.4): Comparison of p_c for the square and triangular lattices using the Aizenman-Grimmett method. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. Etwas weiter unten hat unser Testerteam auch noch eine hilfreiche Checkliste für den Kauf aufgestellt - Sodass Sie als Käufer unter der großen Auswahl an Probability topics der Probability topics ausfindig machen können, die in jeder Hinsicht zu Ihrer Person passen wird! Editor and writer. Lecture 12 (11.6): Super-critical percolation in dimensions 3 and higher: Proof that P(n≤|C_0|

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