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math.PR2020
Random Lie Brackets that Induce Torsion: A Model for Noisy Vector Fields
Didong Li, Sayan Mukherjee
We define and study a random Lie bracket that induces torsion in expectation. Almost all stochastic analysis on manifolds have assumed parallel transport. Mathematically this assum…
math.PR2013★ 56 cited
Probabilistic Fréchet Means for Time Varying Persistence Diagrams
Elizabeth Munch, Katharine Turner, Paul Bendich +3
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In 2011, Mileyko and his…
math.PR2013
The Topology of Probability Distributions on Manifolds
Omer Bobrowski, Sayan Mukherjee
Let be a set of random points in , generated from a probability measure on a -dimensional manifold . In this paper we study the homology of …