On discrete loop signatures and Markov loops topology

Yves Le Jan (1)

1 Département de Mathématiques [ORSAY]

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.

Domaines: Probabilités [math.PR]

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