TY - JOUR

T1 - Functional Central Limit Theorems and P(ϕ)1-Processes for the Relativistic and Non-Relativistic Nelson Models

AU - Gheryani, Soumaya

AU - Hiroshima, Fumio

AU - Lőrinczi, József

AU - Majid, Achref

AU - Ouerdiane, Habib

N1 - Funding Information:
FH is financially supported by JSPS Open Partnership Joint Projects between Japan and Tunisia “Non-commutative infinite dimensional harmonic analysis: A unified approach from representation theory and probability theory”, and is also supported by Grant-in-Aid for Scientific Research (B)16H03942 and Grant-in-Aid for Scientific Research (B)20H01808 from JSPS.
Funding Information:
FH is financially supported by JSPS Open Partnership Joint Projects between Japan and Tunisia ?Non-commutative infinite dimensional harmonic analysis: A unified approach from representation theory and probability theory?, and is also supported by Grant-in-Aid for Scientific Research (B)16H03942 and Grant-in-Aid for Scientific Research (B)20H01808 from JSPS.
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85084412719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85084412719&partnerID=8YFLogxK

U2 - 10.1007/s11040-020-09345-3

DO - 10.1007/s11040-020-09345-3

M3 - Article

AN - SCOPUS:85084412719

SN - 1385-0172

VL - 23

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

IS - 2

M1 - 18

ER -