In this talk I will discuss a probabilistic theory of convergence between a random mapper graph and the Reeb graph. I will outline the construction of an enhanced mapper graph associated to points randomly sampled from a probability density function concentrated on a constructible R-space. I will then explain how interleaving distances for constructible cosheaves and topological estimations via kernel density estimates can be used to show that the enhanced mapper graph approximates the Reeb graph in a precise way. The content of the talk is joint work with Omer Bobrowski, Elizabeth Much, and Bei Wang.

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