On discrete loop signatures and Markov loops topology

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. This last result has yet to be extended to higher order homologies.
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https://hal.archives-ouvertes.fr/hal-02265642
Contributor : Yves Le Jan <>
Submitted on : Sunday, August 11, 2019 - 8:53:16 AM
Last modification on : Wednesday, August 14, 2019 - 1:10:47 AM

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Yves Le Jan. On discrete loop signatures and Markov loops topology. 2019. ⟨hal-02265642⟩

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