Spring 2017
General Information
Syllabus
Lectures
Homework
Lectures
1/24/17. Lecture 1: Measure theory background.1/26/17. Lecture 2: Differentiation, product measures, independence.
1/31/17. Lecture 3: The law of large numbers.
2/2/17. Lecture 4: Convergence of random series and large deviations.
2/7/17. Lecture 5: Characteristic functions, central limit theorems.
2/14/17. Lecture 6: Rates of convergence, the local limit theorem, Poisson approximation.
2/16/17. Lecture 7: Stein's method.
2/21/17. Lecture 8: Limit laws, introduction to random walk.
2/23/17. Lecture 9: Recurrence, renewals.
2/28/17. Lecture 10: Intro to martingales.
3/3/17. Lecture 11: Convergence of martingales.
3/21/17. Lecture 12: Markov chains.
3/23/17. Lecture 13: Stationary measures, the hypercube, riffle shuffles.
3/28/17. Lecture 14: Ergodic theory.
4/4/17. Lecture 15: Multiple ergodic averages of finite complexity.
4/6/17. Lecture 16: Equidistribution on nilmanifolds.
4/13/17. Lecture 17: Brownian motion.
4/18/17. Lecture 18: Brownian motion as a Markov process.
4/20/17. Lecture 19: Harmonic functions and applications.
4/25/17. Lecture 20: Hausdorff dimension.
4/27/17. Lecture 21: Brownian motion and random walk.
5/5/17. Lecture 22: Concentration of measure.
5/9/17. Lecture 23: Stochastic integration.
5/11/17. Lecture 24: The Gaussian free field and Liouville quantum gravity.
Content of some slides closely follows Durrett and/or Morters and Peres.