Oct. 29, 3:30pm, Wean 8220

Swastik Kopparty, Rutgers University

A local central limit theorem for triangles in a random graph

Swastik Kopparty, Rutgers University

A local central limit theorem for triangles in a random graph

Abstract:

What is the distribution of the number of triangles in the random graph *G*(*n*, *1*/*2*)? It was known for a long time that this distribution obeys a central limit theorem: from the point of view of large intervals (~standard-deviation length), the distribution looks like a Gaussian random variable. We show that it even obeys a LOCAL central limit theorem: the distribution is pointwise close to a suitable discrete Gaussian random variable.

Joint work with Justin Gilmer