May 21'st in class. Material based on Grimmett's percolation book. Lecture 8 (17.5): The percolation critical point for Z^2 is 1/2 - Zhang's argument and use of the Menshikov / Aizenman-Barsky theorem. Introduction to SLE. Lecture 8 (17.5): The percolation critical point for Z^2 is 1/2 - Zhang's argument and use of the Menshikov / Aizenman-Barsky theorem. in Ghana. Interested in tiny things, nineties nostalgia, old jungle mixtapes, punctuation, and my cats. Supercritical phase: uniqueness of the infinite cluster. Introduction to SLE, arm exponents and scaling relations. Material based on Grimmett's percolation book. Material based on Grimmett's percolation and probability on graphs book. The course is on Percolation Theory, with a focus on percolation on Euclidean lattices such as Z^d. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. Exercise 1. In order to make it easier to generate lively discussions during our class sessions!) Material based on Grimmett's percolation book. Material based on Grimmett's percolation book. The second volume is on theoretical distributions, including Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Multinomial, Uniform, Exponential, Gamma, Beta and Normal Distributions. Right continuity of theta(p) on [0,1]. 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. The exercise needs to be handed in by Material based on Grimmett's percolation book. Material based on Grimmett's percolation book and discussions with Gady Kozma. 'I�+ݕ����ڸ����h%'���}�@���]��,�=���F/��L��kV����} Lecture 9 (21.5 - only two hours): Cardy's formula and its history. Exercise 9. Proof of statements for large enough p. Definition of slab critical point. Lecture 4 (19.3): Description of general FKG inequality. Spring; Exam form. April 9'th in class. Lecture 8 (17.5): The percolation critical point for Z^2 is 1/2 - Zhang's argument and use of the Menshikov / Aizenman-Barsky theorem. Lecture 1 (26.2): Introduction, Galton-Watson trees (survival has positive probability if and only if mean offspring number is at least 1). Lecture 9 (21.5 - only two hours): Cardy's formula and its history. Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on Tumblr (Opens in new window), Click to share on Reddit (Opens in new window), Click to email this to a friend (Opens in new window), Creative Commons Attribution-NonCommercial 3.0 Unported License. Lecture 12 (11.6): Super-critical percolation in dimensions 3 and higher: Proof that P(n≤|C_0|p_c(Z^d) using static renormalization results. Beginning of the proof of Smirnov's theorem. Introduction to the Grimmett-Marstrand theorem and its proof. Material based on Grimmett's percolation book and discussions with Gady Kozma. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. Lecture 11 (4.6): Super-critical percolation in dimensions 3 and higher: Some statements without proof - p_c(half space) = p_c(Z^d), P(0distance n, but not to infinity) decays exponentially, P(n≤|C_0|�W�[u P� =J���M�/E�O'�9y �P�_'��%z�bU�U������@#�O\���q�����QNNa¨��E�p7e2u:���͒�pwOsXn0מ �0T]�,*����)��i��'��� �B&U�M�:=��B�=/�OȌ��^�4�u:F;�c`I���/X.M�sZ�0�3߫`�k�#�>�U6�T�!5�h545v7c cU� ���{k��-�. Uniqueness of the infinite cluster in super-critical percolation. Introduction to conformal invariance. /ProcSet [ /PDF /Text ] These lessons on probability will include the following topics: Samples in probability, Probability of events, Theoretical probability, Experimental probability, Probability problems, Tree diagrams, Mutually exclusive events, Independent events, Dependent events, Factorial, Permutations, Combinations, Probability in Statistics, Probability and Combinatorics. Lecture 13 (18.6): (Most of the) proof of the Grimmett-Marstrand theorem. Material based on Grimmett's percolation book. Was für ein Ziel visieren Sie als Benutzer mit seiner Probability topics an? Not to be fed after midnight. Material based on Grimmett's percolation book and discussions with Gady Kozma. 1 0 obj Lecture 9 (21.5 - only two hours): Cardy's formula and its history. Introduction to conformal invariance. Exercise 3. Beginning of the proof of Aizenman-Barsky to the Aizenman-Barsky / Menshikov theorem. Location: Dan David 204, Tuesdays 10-13. /Length 299 Material based on Grimmett's percolation book. Change ), You are commenting using your Twitter account. Material based on Grimmett's percolation book. Galton-Watson trees and percolation on trees. Stochastic Processes (Advanced Probability II), 36-754 Spring 2007 TuTh 9:00--10:20, in 232Q Baker Hall Prof. Cosma Shalizi. Material based on Grimmett's percolation book and discussions with Gady Kozma. Material based on Grimmett's percolation book and discussions with Gady Kozma. Russo-Seymour-Welsh for the triangular lattice. Lecture 9 (21.5 - only two hours): Cardy's formula and its history. Blog about economic history & comparative development, We hike, bike, and discover Central Florida and beyond, A blog about economics, politics and the random interests of forty-something professors. PREFACE These course notes have been revised based on my past teaching experience at the department of Biostatistics in the University of North Carolina in Fall 2004 and Fall 2005. Beginning of the proof of Harris inequality (FKG for percolation). Description of Reimer's inequality. /Filter /FlateDecode Beginning of the proof of Aizenman-Barsky to the Aizenman-Barsky / Menshikov theorem. Material based on Grimmett's percolation and probability on graphs book. Material based on Grimmett's percolation book. Professor Nicholas N. N. Nsowah–Nuamah, a full Professor of Statistics Material based on Grimmett's percolation book. Lecture 11 (4.6): Super-critical percolation in dimensions 3 and higher: Some statements without proof - p_c(half space) = p_c(Z^d), P(0distance n, but not to infinity) decays exponentially, P(n≤|C_0|p_c. Right continuity of theta(p) on [0,1]. Tasks: There will be several homework assignments. Exercise 4. It overlaps with the (alphabetical) list of statistical topics. April 23'rd in class. (the “facemash” sequence in The Social Network), Class #12: Pending SCOTUS Case (we will discuss one or more of the cases that are currently pending before the Supreme Court), Class #13: Exit Interviews (students will split up into pairs and each duo will choose a legal or ethical puzzle to discuss). Material based on Grimmett's percolation book. Introduction to the Grimmett-Marstrand theorem and its proof. Supercritical phase: uniqueness of the infinite cluster.

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