Interactions Between Trees and Loops, and Their Representation in Fock Space

Yves Le Jan

doi:10.1007/978-981-19-4672-1_16

Interactions Between Trees and Loops, and Their Representation in Fock Space

Yves Le Jan

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

It has been observed that on a weighted graph, an extension of Wilson’s algorithm provides an independent pair (T, L), T being a spanning tree and L a Poissonian loop ensemble. This association can be interpreted in the framework of symmetric and skew symmetric Fock spaces. Given a weighted graph, we show how to define a natural interaction between the random spanning tree and the loop ensemble, which corresponds to a local interaction between two Fock spaces.

Original language	English (US)
Title of host publication	Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
Editors	Zhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
Publisher	Springer
Pages	309-319
Number of pages	11
ISBN (Print)	9789811946714
DOIs	https://doi.org/10.1007/978-981-19-4672-1_16
State	Published - 2022
Event	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan Duration: Aug 22 2022 → Aug 26 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	394
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
Country/Territory	Japan
City	Osaka
Period	8/22/22 → 8/26/22

Keywords

Fock space
Free fields
Markov loops
Spanning trees

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-981-19-4672-1_16

Cite this

Interactions Between Trees and Loops, and Their Representation in Fock Space. / Le Jan, Yves.
Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. ed. / Zhen-Qing Chen; Masayoshi Takeda; Toshihiro Uemura. Springer, 2022. p. 309-319 (Springer Proceedings in Mathematics and Statistics; Vol. 394).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Le Jan, Y 2022, Interactions Between Trees and Loops, and Their Representation in Fock Space. in Z-Q Chen, M Takeda & T Uemura (eds), Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. Springer Proceedings in Mathematics and Statistics, vol. 394, Springer, pp. 309-319, International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022, Osaka, Japan, 8/22/22. https://doi.org/10.1007/978-981-19-4672-1_16

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AB - It has been observed that on a weighted graph, an extension of Wilson’s algorithm provides an independent pair (T, L), T being a spanning tree and L a Poissonian loop ensemble. This association can be interpreted in the framework of symmetric and skew symmetric Fock spaces. Given a weighted graph, we show how to define a natural interaction between the random spanning tree and the loop ensemble, which corresponds to a local interaction between two Fock spaces.

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Interactions Between Trees and Loops, and Their Representation in Fock Space

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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