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

Yves Le Jan

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationDirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
EditorsZhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
PublisherSpringer
Pages309-319
Number of pages11
ISBN (Print)9789811946714
DOIs
StatePublished - 2022
EventInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan
Duration: Aug 22 2022Aug 26 2022

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume394
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
Country/TerritoryJapan
CityOsaka
Period8/22/228/26/22

Keywords

  • Fock space
  • Free fields
  • Markov loops
  • Spanning trees

ASJC Scopus subject areas

  • Mathematics(all)

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