Brownian Loops Topology

Yves Le Jan

doi:10.1007/s11118-019-09765-z

Brownian Loops Topology

Yves Le Jan

Mathematics

Research output: Contribution to journal › Article › peer-review

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).

Original language	English (US)
Pages (from-to)	223-229
Number of pages	7
Journal	Potential Analysis
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s11118-019-09765-z
State	Published - Jun 1 2020

Keywords

Holonomy
Markov loops

ASJC Scopus subject areas

Analysis

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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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AB - 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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KW - Markov loops

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Brownian Loops Topology

Abstract

Keywords

ASJC Scopus subject areas

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