Counting Random Graphs

Start Date: November 8, 2023
Event Start Time: 12:15 PM
Event End Time: 1:15 PM
Seminar Series: Graduate Combinatorics Seminar
Presenter(s): Brian Pinsky - Rutgers University
Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
Presentation Type: Stand Alone Presentation
Abstract:
What is the probability the following graphs are isomorphic?
1. Two random graphs random graphs on n verticies with probability p.
2. Two random graphs random graphs on $\mathbb {N}$ verticies with probability p.
3. Two random graphs random graphs on $\mathbb {N}$ ^ $\mathbb {N}$ verticies with probability p.
Question 1 is way too hard for me; I will say nothing about it.

Question 2 is easy, and we will answer it Wednesday. That will be the required amount of real mathematical content, hopefully.

My real goal is to answer question 3. It's almost certainly ill-posed, and we will need to rethink what probability even means in the first place to answer this. However, the answer is probably 0.

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