Graduate student reading seminar: Difference between revisions
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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. | 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. Let <math>\tau_N</math> be the hitting time of the boundary of <math>B_N</math>. Show that <math>P(X_{\tau_N}\in E_N)\to 1</math> | ||
Revision as of 21:53, 17 February 2012
Time and place: Friday 2:30PM-4PM, B211
Electrical networks
Random Walks and Electric Networks by Doyle and Snell
Probability on Trees and Networks by Russell Lyons with Yuval Peres
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]\displaystyle{ B_N=[-N,N]^2 }[/math] and let [math]\displaystyle{ 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]\displaystyle{ 1/4-\epsilon, 1/4, 1/4+\epsilon, 1/4 }[/math] for the W, N, E and S directions. Let [math]\displaystyle{ \tau_N }[/math] be the hitting time of the boundary of [math]\displaystyle{ B_N }[/math]. Show that [math]\displaystyle{ P(X_{\tau_N}\in E_N)\to 1 }[/math]
Fall 2011
Determinantal point processes
Determinantal point processes: Chapters 4 and 6
Determinantal random point fields by Alexander Soshnikov
Terry Tao's blog entry on determinantal point processes
Random matrices and determinantal processes by K. Johansson
Determinantal point processes by A. Borodin
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 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
Random Walks and Electric Networks by Doyle and Snell
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