Difference between revisions of "Graduate student reading seminar"

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(Stochastic Calculus)
(Replacing page with 'Time and place: Monday 2:25PM-3:30PM, ??? We decided to start with SLE (Sctochastic Loewner evolution). We will use Greg Lawler's [http://math.uchicago.edu/~lawler/utah.pdf Pa...')
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Time and place: Friday 2:30PM-4PM, B211
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Time and place: Monday 2:25PM-3:30PM, ???
  
== Electrical networks ==
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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]
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September 17: read Lecture 1 from the notes
 
 
February 3: Review 2.1 and 2.2 from the Lyons-Peres book and read 2.3
 
 
 
February 10: Read 2.4 and  start reading 2.5
 
 
 
February 17: Read 2.5
 
 
 
February 24: Read 2.6
 
 
 
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?
 
 
 
 
 
== Stochastic Calculus ==
 
 
 
March 2: Read the first section of the lecture notes.
 
March 9: Read the second section.
 
March 16: 3rd section (up to Ito integrals)
 
 
 
== Fall 2011 ==
 
 
 
 
 
==Determinantal point processes==
 
 
 
[http://research.microsoft.com/en-us/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]
 
 
 
Determinantal point processes: Chapters 4 and 6
 
 
 
[http://www.i-journals.org/ps/viewarticle.php?id=41 Determinantal processes and independence by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres]
 
 
 
[http://arxiv.org/abs/math/0002099 Determinantal random point fields by Alexander Soshnikov]
 
 
 
[http://terrytao.wordpress.com/2009/08/23/determinantal-processes/ Terry Tao's blog entry on determinantal point processes]
 
 
 
[http://arxiv.org/abs/math-ph/0510038  Random matrices and determinantal processes by K. Johansson ]
 
 
 
[http://arxiv.org/abs/0911.1153  Determinantal point processes by A. Borodin ]
 
 
 
[http://mypage.iu.edu/~rdlyons/pdf/bases.pdf Determinantal probability measures by R. Lyons]
 
 
 
September 13: start reading the HKPV book (Chapter 4). You can also have a look at the other survey articles listed above.
 
 
 
September 20: finish Section 4.2 and go through the first example in 4.3 (non-intersecting random walks)
 
 
 
September 27: Corollary 4.3.3, the rest of the examples in 4.3 and 4.4 (how to generate determinantal processes)
 
 
 
October 4: there is no reading seminar (you should go to the [[Probability_Seminar|Probability Seminar]] instead)
 
 
 
October 11: start reading Section 4.5
 
 
 
October 18: existence and the necessary and sufficient condition (4.5)
 
 
 
October 25: there is no reading seminar this week
 
 
 
November 1: simultaneously observable subsets (end of 4.5), 4.6-4.8
 
 
 
November 8: High powers of complex polynomial processes (4.8), uniform spanning trees (6.1)
 
 
 
November 15: Uniform spanning trees cont. (6.1)
 
 
 
November 22: Ginibre ensemble, circular ensemble (.2, 6.4)
 
 
 
== Electrical networks ==
 
 
 
[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]
 
 
 
December 6: Electrical networks. Start reading Chapter 2 of the Lyons-Peres book.
 
 
 
December 13: Continue reading Chapter 2
 

Revision as of 14:59, 7 September 2012

Time and place: Monday 2:25PM-3:30PM, ???

We decided to start with SLE (Sctochastic Loewner evolution). We will use Greg Lawler's Park City notes.


September 17: read Lecture 1 from the notes