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−  Time and place: Friday 2:30PM4PM, B211  +  Time and place: Monday 2:25PM3:30PM, ??? 
   
−  == Electrical networks ==
 +  We decided to start with SLE (Sctochastic Loewner evolution). We will use Greg Lawler's [http://math.uchicago.edu/~lawler/utah.pdf Park City notes]. 
   
−  [http://www.math.dartmouth.edu/~doyle/docs/walks/walks.pdf Random Walks and Electric Networks by Doyle and Snell]
 
   
−  [http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html Probability on Trees and Networks by Russell Lyons with Yuval Peres]
 +  September 17: read Lecture 1 from the notes 
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−  February 3: Review 2.1 and 2.2 from the LyonsPeres book and read 2.3
 
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−  February 10: Read 2.4 and start reading 2.5
 
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−  February 17: Read 2.5
 
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−  February 24: Read 2.6
 
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−  HW problem: Let <math> B_N=[N,N]^2</math> and let <math>E_N=\{(x,y): x=N, y\le N\}</math> the east side of this box. Consider a simple RW started at (0,0) on the lattice where the jump probabilities are <math>1/4\epsilon, 1/4, 1/4+\epsilon, 1/4</math> for the W, N, E and S directions (<math>\epsilon >0</math> is fixed). Let <math>\tau_N</math> be the hitting time of the boundary of <math>B_N</math>. Show using the machinery of electrical networks that <math>P(X_{\tau_N}\in E_N)\to 1</math>. How can you change the aspect ratio of the box so the result stays true?
 
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−  == Stochastic Calculus ==
 
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−  March 2: Read the first section of the lecture notes.
 
−  March 9: Read the second section.
 
−  March 16: 3rd section (up to Ito integrals)
 
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−  == Fall 2011 ==
 
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−  ==Determinantal point processes==
 
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−  [http://research.microsoft.com/enus/um/people/peres/GAF_book.pdf Zeros of Gaussian Analytic Functions and Determinantal Point Processes by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres]
 
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−  Determinantal point processes: Chapters 4 and 6
 
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−  [http://www.ijournals.org/ps/viewarticle.php?id=41 Determinantal processes and independence by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres]
 
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−  [http://arxiv.org/abs/math/0002099 Determinantal random point fields by Alexander Soshnikov]
 
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−  [http://terrytao.wordpress.com/2009/08/23/determinantalprocesses/ Terry Tao's blog entry on determinantal point processes]
 
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−  [http://arxiv.org/abs/mathph/0510038 Random matrices and determinantal processes by K. Johansson ]
 
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−  [http://arxiv.org/abs/0911.1153 Determinantal point processes by A. Borodin ]
 
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−  [http://mypage.iu.edu/~rdlyons/pdf/bases.pdf Determinantal probability measures by R. Lyons]
 
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−  September 13: start reading the HKPV book (Chapter 4). You can also have a look at the other survey articles listed above.
 
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−  September 20: finish Section 4.2 and go through the first example in 4.3 (nonintersecting random walks)
 
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−  September 27: Corollary 4.3.3, the rest of the examples in 4.3 and 4.4 (how to generate determinantal processes)
 
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−  October 4: there is no reading seminar (you should go to the [[Probability_SeminarProbability Seminar]] instead)
 
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−  October 11: start reading Section 4.5
 
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−  October 18: existence and the necessary and sufficient condition (4.5)
 
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−  October 25: there is no reading seminar this week
 
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−  November 1: simultaneously observable subsets (end of 4.5), 4.64.8
 
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−  November 8: High powers of complex polynomial processes (4.8), uniform spanning trees (6.1)
 
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−  November 15: Uniform spanning trees cont. (6.1)
 
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−  November 22: Ginibre ensemble, circular ensemble (.2, 6.4)
 
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−  == Electrical networks ==
 
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−  [http://www.math.dartmouth.edu/~doyle/docs/walks/walks.pdf Random Walks and Electric Networks by Doyle and Snell]
 
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−  [http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html Probability on Trees and Networks by Russell Lyons with Yuval Peres]
 
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−  December 6: Electrical networks. Start reading Chapter 2 of the LyonsPeres book.
 
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−  December 13: Continue reading Chapter 2
 