Brownian Loops Topology

Yves Le Jan

Research output: Contribution to journalArticlepeer-review


In the seminal work of Symanzik (1969), Poisson ensembles of Brownian loops were implicitly used. Since the work of Lawler and Werner (Prob. Th. Rel. Fields 128:565–588 2004) on “loop soups”, these ensembles have also been the object of many investigations. The purpose of the present work is to determine the distributions related to their topological properties, using trace formula and zeta regularization. These results have been announced in Le Jan (2016) and Le Jan (2017).

Original languageEnglish (US)
Pages (from-to)223-229
Number of pages7
JournalPotential Analysis
Issue number1
StatePublished - Jun 1 2020


  • Holonomy
  • Markov loops

ASJC Scopus subject areas

  • Analysis


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