Description
A poset P is a set X equipped with a partial order. A causal set is a locally finite poset, which was introduced to model the space-time universe in physics. In this talk I will briefly review the literature of different models on random orders and their relations to causal set theory. Then we focus on an open problem proposed by Erdos on the evolution of the dimensions of random graph orders. The random graph order is a type of classical sequential growth model that physicists use to generate a random causal set.
The dimension of a poset P is the minimum number of linear orderings required whose intersection is P. The dimensions of the random graph orders have 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 complete the last piece of the puzzle by determining their asymptotic behaviours in the sparse regime.
This talk is based on a collaborated work with Arnav Kumar.
