On discrete loop signatures and Markov loops topology

Yves Le Jan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2021-2036
Number of pages16
JournalRevista Matematica Iberoamericana
Issue number5
StatePublished - 2021


  • Loop signatures
  • Markov loops

ASJC Scopus subject areas

  • General Mathematics


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