## EVENT DETAILS AND ABSTRACT

**Probability Seminar**
**Title:** The scaling limit of a critical random directed graph

**Speaker:** Christina Goldschmidt

**Speaker Info:** Oxford University

**Brief Description:**

**Special Note**:

**Abstract:**

We consider the random directed graph D(n, p) with vertex set {1, 2, . . . , n} in which each of the n(n − 1) possible directed edges is present independently with probability p. We are interested in the strongly connected components of this directed graph. A phase transition for the emergence of a giant strongly connected component is known to occur at p = 1/n, with critical window p = 1/n + \lambda n^{-4/3} for \lambda \in \R. We show that, within this critical window, the strongly connected components of D(n, p), ranked in decreasing order of size and rescaled by n^{-1/3}, converge in distribution to a sequence of finite strongly connected directed multigraphs with edge lengths which are either 3-regular or loops. This is joint work with Robin Stephenson (Sheffield).

**Date:** Wednesday, May 05, 2021

**Time:** 9:00am

**Where:** https://northwestern.zoom.us/j/907400031

**Contact Person:** Antonio Auffinger

**Contact email:** tuca@northwestern.edu

**Contact Phone:**

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