Title:Evolution of random graph orders and their dimensions
| Speaker: | Jane Gao |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: A poset is a set X equipped with a partial order. In this talk I will briefly review the literature of different models on random orders. Then we discuss a particular model called the random graph order. The random graph order is classical model to generate a random causal set, which was introduced in physics to model and analyse the space-time universe.
We will focus on an open problem proposed by Erdos, Kierstad and Trotter on the evolution of the dimensions of random graph orders. This problem has been studied by Albert and Frieze, and by Erdos, Kierstad and Trotter around 1990. Better bounds on the dimensions were obtained by Bollobas and Brightwell in 1997, for “non-sparse” random graph orders. We study the last piece of the puzzle, in the bipartite case, by investigating “a transition phase” that was predicted to occur in the sparse regime by Bollobas and Brightwel, and we prove a negative result to their prediction. We expect that a similar phenomenon would occur in the nonbipartite case.
This talk is based on a collaborated work with Arnav Kumar.