On discrete loop signatures and Markov loops topology

Yves Le Jan

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arXiv · 1908.05187

On discrete loop signatures and Markov loops topology

Yves Le Jan

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Abstract

Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop homotopy class, and of the first and second homologies, defined by the lower central series of the fundamental group.

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Yves Le Jan. 2019-08-14. On discrete loop signatures and Markov loops topology. https://arxiv.org/abs/1908.05187

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