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Explore two general models of random simplicial complexes that extend the Erdos-Renyi model for random graphs in this comprehensive lecture. Delve into the probabilistic models of random simplicial complexes from Costa-Farber, Kahle, and Linial-Meshulam as special cases. Examine the Alexander duality relation between these models and its implications for information transfer. Investigate the limitations of this duality with vanishing probability parameters and its effectiveness when parameters are uniformly bounded. Learn about the Rado simplicial complex, the unique infinite random simplicial complex. Gain insights from joint work with Michael Farber, Tahl Nowik, and Lewin Strauss in this advanced exploration of algebraic topology and probability theory.
