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.
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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 -