The Bulk and the Extremes of Online Minimal Spanning Acycles

Explore the distributional properties of weights in random Minimum Spanning Acycles (MSAs) through this 57-minute lecture from the Applied Algebraic Topology Network. Delve into the extension of Frieze's classic result on Minimum Spanning Trees to higher-dimensional simplicial complex models. Examine both the bulk and extreme behaviors of MSA weights, with a focus on the online setting where only partial face weight information is available. Discover how the empirical distribution of MSA weights in the bulk converges to a measure based on the giant shadow, the higher-dimensional analogue of the giant component. Learn about the convergence of extremal weights to an inhomogeneous Poisson point process. Gain insights into this advanced topic in applied algebraic topology and its connections to random graph theory and probabilistic combinatorics.