Random and Quasirandom Simulation: Lectures

Go to http://echo360.uml.edu/propp2014/stochasticprocess.html to view videos of individual lectures. (The videos used to be, and might still be, be available from http://echo360.uml.edu/propp; to use that site you will need to enter your UML user name and password.)

(The lectures from 2007 and the lectures from 2008 are still available on-line, although there will be many differences between the 2007 and 2008 versions of the course and the 2010 version of the course, and I suspect some of the videos have been deleted.)

Most of my lecture notes are embedded in Mathematica notebooks, along with Mathematica code that implements the algorithms under discussion. If you can't open the notebooks, or can't run the code, on account of not having Mathematica, fear not! Wolfram Research has just announced a new service that makes it possible to share Mathematica notebooks with anyone, whether or not they have Mathematica: "Using the new Publish for Player site, you can now convert your interactive notebooks for use with the free Mathematica Player." I haven't taken the time to do this, but if any of you want me to, let me know!

To view a section of a a Mathematica notebook, double-click on the bracket to the right of the caption. To close the section, select the appropriate bracket and double-click on it.

Also, I have created pdf version of the Mathematica notebooks.

Lecture #1: Random and Quasirandom Simulation. [Mathematica notebook Lec01.nb] [PDF file Lec01.pdf]

Lecture #2: Random Variables (Review). Quasirandomness demo. [Mathematica notebook Lec02.nb] [PDF file Lec02.pdf] [Rotor-router applet]

Lecture #3: Absorbing Markov chains. [Mathematica notebook Lec03.nb] [PDF file Lec03.pdf]

Lecture #4: Absorbing Markov chains (continued). [Mathematica notebook Lec04.nb] [PDF file Lec04.pdf]

Lecture #5: Ergodic Markov chains. [Mathematica notebook Lec05.nb] [PDF file Lec05.pdf]

Lecture #6: Ergodic Markov chains. Examples of Markov chains. [Mathematica notebook Lec06.nb] [PDF file Lec06.pdf]

Lecture #7: Rotor-routing. Sampling from a specified distribution. [Mathematica notebook Lec07.nb] [PDF file Lec07.pdf]

Lecture #8: Random walk and queueing models. [Mathematica notebook Lec08.nb] [PDF file Lec08.pdf]

Lecture #9: Diffusion-driven processes, mixing time, and stopping rules. [Mathematica notebook Lec09.nb] [PDF file Lec09.pdf]

Lecture #10: Exact sampling, importance sampling, and Poisson processes. [Mathematica notebook Lec10.nb] [PDF file Lec10.pdf]

Lecture #11: Poisson processes and Brownian motion. [Mathematica notebook Lec11.nb] [PDF file Lec11.pdf]

Lecture #12: Brownian motion. [Mathematica notebook Lec12.nb] [PDF file Lec12.pdf]

Lecture #13: Electrical networks and random walk. [Mathematica notebook Lec13.nb] [PDF file Lec13.pdf]