https://hilbert.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Jkrush&feedformat=atomUW-Math Wiki - User contributions [en]2021-03-07T03:41:27ZUser contributionsMediaWiki 1.30.1https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_student_reading_seminar&diff=12344Graduate student reading seminar2016-09-17T11:06:49Z<p>Jkrush: /* 2016 Fall */</p>
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<div>==2016 Fall==<br />
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Tuesday, 2:25pm, Room 348 Birge Hall<br />
<br />
Preliminary schedule (to be updated as needed)<br />
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9/27 Daniele?<br />
<br />
10/4 Jessica<br />
<br />
10/11, 10/18: Dae Han<br />
<br />
10/25, 11/1: Jinsu<br />
<br />
11/8, 11/15: Hans<br />
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11/22, 11/29: Keith<br />
<br />
Surprisingly Determinental: DPPs and some asymptotics of ASEP <br />
<br />
I'll be reading and presenting some recent papers of Alexei Borodin and a few collaborators which have uncovered certain equivalences between determinental point processes and non-determinental processes.<br />
<br />
12/6, 12/13: Fan<br />
<br />
==2016 Spring==<br />
<br />
Tuesday, 2:25pm, B321 Van Vleck<br />
<br />
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3/29, 4/5: Fan Yang<br />
<br />
I will talk about the ergodic decomposition theorem (EDT). More specifically, given a compact metric space X and a continuous transformation T on it, the theorem shows that any T-invariant measure on X can be decomposed into a convex combination of ergodic measures. In the first talk I introduced the EDT and some related facts. In the second talk, I will talk about the conditional measures, and prove that the ergodic measures in EDT are indeed the conditional measures.<br />
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<br />
2/16 : Jinsu<br />
<br />
Lyapunov function for Markov Processes.<br />
<br />
For ODE, we can show stability of the trajectory using Lyapunov functions.<br />
<br />
There is an analogy for Markov Processes. I'd like to talk about the existence of stationary distribution with Lyapunov function.<br />
<br />
In some cases, it is also possible to show the rate of convergence to the stationary distribution.<br />
<br />
==2015 Fall==<br />
<br />
This semester we will focus on tools and methods.<br />
<br />
[https://www.math.wisc.edu/wiki/images/a/ac/Reading_seminar_2015.pdf Seminar notes] ([https://www.dropbox.com/s/f4km7pevwfb1vbm/Reading%20seminar%202015.tex?dl=1 tex file], [https://www.dropbox.com/s/lg7kcgyf3nsukbx/Reading_seminar_2015.bib?dl=1 bib file])<br />
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9/15, 9/22: Elnur<br />
<br />
I will talk about large deviation theory and its applications. For the first talk, my plan is to introduce Gartner-Ellis theorem and show a few applications of it to finite state discrete time Markov chains.<br />
<br />
9/29, 10/6, 10/13 :Dae Han<br />
<br />
10/20, 10/27, 11/3: Jessica<br />
<br />
I will first present an overview of concentration of measure and concentration inequalities with a focus on the connection with related topics in analysis and geometry. Then, I will present Log-Sobolev inequalities and their connection to concentration of measure. <br />
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11/10, 11/17: Hao Kai<br />
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11/24, 12/1, 12/8, 12/15: Chris<br />
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: <br />
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2016 Spring:<br />
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2/2, 2/9: Louis<br />
<br />
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2/16, 2/23: Jinsu<br />
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3/1, 3/8: Hans<br />
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==2015 Spring==<br />
<br />
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2/3, 2/10: Scott<br />
<br />
An Introduction to Entropy for Random Variables<br />
<br />
In these lectures I will introduce entropy for random variables and present some simple, finite state-space, examples to gain some intuition. We will prove the <br />
MacMillan Theorem using entropy and the law of large numbers. Then I will introduce relative entropy and prove the Markov Chain Convergence Theorem. Finally I will <br />
define entropy for a discrete time process. The lecture notes can be found at http://www.math.wisc.edu/~shottovy/EntropyLecture.pdf.<br />
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2/17, 2/24: Dae Han<br />
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3/3, 3/10: Hans<br />
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3/17, 3/24: In Gun<br />
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4/7, 4/14: Jinsu<br />
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4/21, 4/28: Chris N.<br />
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==2014 Fall==<br />
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9/23: Dave<br />
<br />
I will go over Mike Giles’ 2008 paper “Multi-level Monte Carlo path simulation.” This paper introduced a new Monte Carlo method to approximate expectations of SDEs (driven by Brownian motions) that is significantly more efficient than what was the state of the art. This work opened up a whole new field in the numerical analysis of stochastic processes as the basic idea is quite flexible and has found a variety of applications including SDEs driven by Brownian motions, Levy-driven SDEs, SPDEs, and models from biology<br />
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9/30: Benedek<br />
<br />
A very quick introduction to Stein's method. <br />
<br />
I will give a brief introduction to Stein's method, mostly based on the the first couple of sections of the following survey article:<br />
<br />
Ross, N. (2011). Fundamentals of Stein’s method. Probability Surveys, 8, 210-293. <br />
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The following webpage has a huge collection of resources if you want to go deeper: https://sites.google.com/site/yvikswan/about-stein-s-method<br />
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<br />
Note that the Midwest Probability Colloquium (http://www.math.northwestern.edu/mwp/) will have a tutorial program on Stein's method this year. <br />
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10/7, 10/14: Chris J.<br />
[http://www.math.wisc.edu/~janjigia/research/MartingaleProblemNotes.pdf An introduction to the (local) martingale problem.]<br />
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10/21, 10/28: Dae Han<br />
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11/4, 11/11: Elnur<br />
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11/18, 11/25: Chris N. Free Probability with an emphasis on C* and Von Neumann Algebras<br />
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12/2, 12/9: Yun Zhai<br />
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==2014 Spring==<br />
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1/28: Greg<br />
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2/04, 2/11: Scott <br />
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[http://www.math.wisc.edu/~shottovy/BLT.pdf Reflected Brownian motion, Occupation time, and applications.] <br />
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2/18: Phil-- Examples of structure results in probability theory.<br />
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2/25, 3/4: Beth-- Derivative estimation for discrete time Markov chains<br />
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3/11, 3/25: Chris J [http://www.math.wisc.edu/~janjigia/research/stationarytalk.pdf Some classical results on stationary distributions of Markov processes]<br />
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4/1, 4/8: Chris N <br />
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4/15, 4/22: Yu Sun<br />
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4/29. 5/6: Diane<br />
<br />
==2013 Fall==<br />
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9/24, 10/1: Chris<br />
[http://www.math.wisc.edu/~janjigia/research/metastabilitytalk.pdf A light introduction to metastability]<br />
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10/8, Dae Han<br />
Majoring multiplicative cascades for directed polymers in random media<br />
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10/15, 10/22: no reading seminar<br />
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10/29, 11/5: Elnur<br />
Limit fluctuations of last passage times <br />
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11/12: Yun<br />
Helffer-Sjostrand representation and Brascamp-Lieb inequality for stochastic interface models<br />
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11/19, 11/26: Yu Sun<br />
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12/3, 12/10: Jason<br />
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==2013 Spring==<br />
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2/13: Elnur <br />
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Young diagrams, RSK correspondence, corner growth models, distribution of last passage times. <br />
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2/20: Elnur<br />
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2/27: Chris<br />
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A brief introduction to enlargement of filtration and the Dufresne identity<br />
[http://www.math.wisc.edu/~janjigia/research/Presentation%20Notes.pdf Notes]<br />
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3/6: Chris<br />
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3/13: Dae Han<br />
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An introduction to random polymers<br />
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3/20: Dae Han<br />
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Directed polymers in a random environment: path localization and strong disorder<br />
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4/3: Diane<br />
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Scale and Speed for honest 1 dimensional diffusions<br />
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References: <br><br />
Rogers & Williams - Diffusions, Markov Processes and Martingales <br><br />
Ito & McKean - Diffusion Processes and their Sample Paths <br><br />
Breiman - Probability <br><br />
http://www.statslab.cam.ac.uk/~beresty/Articles/diffusions.pdf<br />
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4/10: Diane<br />
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4/17: Yun<br />
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Introduction to stochastic interface models<br />
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4/24: Yun<br />
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Dynamics and Gaussian equilibrium sytems<br />
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5/1: This reading seminar will be shifted because of a probability seminar.<br />
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5/8: Greg, Maso<br />
<br />
The Bethe ansatz vs. The Replica Trick. This lecture is an overview of the two <br />
approaches. See [http://arxiv.org/abs/1212.2267] for a nice overview.<br />
<br />
5/15: Greg, Maso<br />
<br />
Rigorous use of the replica trick.</div>Jkrush