Local limit theorems for combinatorial random variables

Combinatorics Seminar
Friday, November 1, 2019 - 11:00am for 1 hour (actually 50 minutes)
Skiles 249
Ross Berkowitz – Yale University – https://rossberkowitz.wordpress.com/
Lutz Warnke

Let X be the number of length 3 arithmetic progressions in a random subset of Z/101Z.  Does X take the values 630 and 640 with roughly the same probability?
Let Y denote the number of triangles in a random graph on n vertices.  Despite looking similar to X, the local distribution of Y is quite different, as Y obeys a local limit theorem.  
We will talk about a method for distinguishing when combinatorial random variables obey local limit theorems and when they do not.