RevisedMS.pdf (200.36 kB)
Functional central limit theorems and P(Φ)₁-processes for the relativistic and non-relativistic Nelson models
journal contribution
posted on 2020-04-21, 14:10 authored by Soumaya Gheryani, Fumio Hiroshima, Jozsef Lorinczi, Achref Majid, Habib OuerdianeWe construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ essentially by sample path regularity. Associated with these processes we define a martingale which, under an appropriate scaling, allows to obtain a central limit theorem for additive functionals of these processes. We discuss a number of examples by choosing specific functionals related to particle-field operators.
Funding
JSPS Open Partnership Joint Projects between Japan and Tunisia “Non-commutative infinite dimensional harmonic analysis: A unified approach from representation theory and probability theory”
Grant-in-Aid for Scientific Research (B)16H03942 and Grant-in-Aid for Scientific Research (B)20H01808 from JSPS
History
School
- Science
Department
- Mathematical Sciences
Published in
Mathematical Physics, Analysis and GeometryVolume
23Publisher
Springer VerlagVersion
- AM (Accepted Manuscript)
Rights holder
© Springer Nature B.V.Publisher statement
This is a post-peer-review, pre-copyedit version of an article published in Mathematical Physics, Analysis and Geometry. The final authenticated version is available online at: https://doi.org/10.1007/s11040-020-09345-3.Acceptance date
2020-04-22Publication date
2020-05-12Copyright date
2020ISSN
1385-0172eISSN
1572-9656Publisher version
Language
- en
Depositor
Dr Jozsef Lorinczi. Deposit date: 18 April 2020Article number
18Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC