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Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, the topology of loops, 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.
Cite this article
Yves Le Jan, On discrete loop signatures and Markov loops topology. Rev. Mat. Iberoam. 37 (2021), no. 5, pp. 2021–2036DOI 10.4171/RMI/1262