MAT 639: Probability I Spring 2017 | |

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## Lectures1/24/17. 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. |

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