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Brownian Loops Topology

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Abstract

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).

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Acknowledgments

Thanks are due to the referee for suggesting several improvements of this paper, and to Jean-Michel Bismut and Yves Benoist for helpful discussions.

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Authors and Affiliations

  1. NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, China

    Yves Le Jan

  2. Département de Mathématique, Université Paris-Sud, Orsay, France

    Yves Le Jan

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  1. Yves Le Jan
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Correspondence to Yves Le Jan.

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Le Jan, Y. Brownian Loops Topology. Potential Anal 53, 223–229 (2020). https://doi.org/10.1007/s11118-019-09765-z

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