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Functional central limit theorems and P(Φ)₁-processes for the relativistic and non-relativistic Nelson models

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posted on 2020-04-21, 14:10 authored by Soumaya Gheryani, Fumio Hiroshima, Jozsef Lorinczi, Achref Majid, Habib Ouerdiane
We 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 Geometry

Volume

23

Publisher

Springer Verlag

Version

  • 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

2020-04-22

Publication date

2020-05-12

Copyright date

2020

ISSN

1385-0172

eISSN

1572-9656

Language

  • en

Depositor

Dr Jozsef Lorinczi. Deposit date: 18 April 2020

Article number

18

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