MATH 7710 Topics in Probability Theory (2022SP)

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Limits Of Discrete Random Structures

Instructor: Lionel Levine

Schedule: Tuesday & Thursday 11:25-12:40

The first class is Tuesday Jan 25. We will meet on Zoom for the first two weeks:
https://cornell.zoom.us/j/98686942029?pwd=K2Qrc25lckpGRnc0bjdFelAxNlEyQT09

Starting Tuesday Feb 8 we will meet in Malott 206.

Lionel's Office Hour: Tuesday 1:30-2:30

There are many ways to take a limit of a discrete structure (such as a random graph, spanning tree, or coloring). We'll explore some of these topics: Random Walks and Electrical Networks, Harmonic Functions, Gaussian Free Field, Scaling Limits, Infinite Volume Limits, Graph Limits (Lovasz and Benjamini-Schramm), Uniform Spanning Forest, Minimal Spanning Forest, Branching Processes, Continuum Random Tree, Concentration Inequalities, Random Graphs, Percolation, Random Cluster Model.
Background: To follow this course you'll need to know at least one semester of graduate probability at the level of MATH 6710.
Familiarity with martingales and Brownian Motion at the level of MATH 6720 is a big plus!
We will follow the book Probability on Trees and Networks, by Lyons and Peres. I expect to cover chapters 2,4,5,6,7,9,10,11,12.
We may also cover parts of the following books:
Random Graphs, by Janson, Luczak, and Rucinski

Zoom Notes

2022-01-25_MATH-7710_Reversible-Markov-Chains-1.pdf 

2022-01-27_MATH-7710_Harmonic-Functions.pdf

2022-02-01_MATH-7710_Electrical-Networks-1.pdf 

2022-02-03_MATH-7710_Energy-Flows-and-Spanning-Trees.pdf  

Notes starting Feb 8 (and the template for notetakers!) are here:

https://canvas.cornell.edu/courses/36345/pages/sign-up-to-take-notes-choose-two-dates

Course Summary:

Date Details Due