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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
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Articles

P(𝜙)1-process for the spin-boson model and a functional central limit theorem for associated additive functionals

Soumaya GheryaniFaculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.
,
Fumio HiroshimaFaculty of Mathematics, Kyushu University, Fukuoka, Japan.
,
József LőrincziDepartment of Mathematical Sciences, Loughborough University, Loughborough, UK.
,
Achref MajidFaculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.Correspondence [email protected]
&
Habib OuerdianeFaculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.
Pages 1104-1115 | Received 10 May 2016, Accepted 21 Aug 2017, Published online: 04 Sep 2017

References

  • A. Arai and M. Hirokawa, On the existence and uniqueness of ground states of generalized spin-boson model, J. Funct. Anal. 151 (1997), pp. 455–503.
  • V. Betz and H. Spohn, A central limit theorem for Gibbs measures relative to Brownian motion, Probab. Theory Rel. Fields 131 (2005), pp. 459–478.
  • A. Boutet de Monvel and J. Sahbani, On the spectral properties of the spin-boson Hamiltonians, Lett. Math. Phys. 44 (1998), pp. 23–33.
  • M. Donsker, An invariance principle for certain probability theorems, Memoirs Amer. Math. Soc. 6 (1951), pp. 1–12.
  • S. Gheryani, F. Hiroshima, J. L\"{o}rinczi, A. Majid, and H. Ouerdiane, Functional central limit theorems and P(ϕ)1-processes for the classical and relativistic Nelson models (2016). Available at arXiv: 1605.0179v1.
  • I. Helland, Central limit theorems for martingales with discrete or continuous time, J. Stat. 20 (1982), pp. 79–94.
  • M. Hirokawa, F. Hiroshima, and J. Lőrinczi, Spin-boson model through a Poisson-driven stochastic process, Math. Z. 277 (2014), pp. 1165–1198.
  • F. Hiroshima, Functional integral approach to semi-relativistic Pauli-Fierz models, Adv. Math. 259 (2014), pp. 784–840.
  • M. Hübner and H. Spohn, Spectral properties of the spin-boson Hamiltonian, Ann. IHP 62 (1995), pp. 289–323.
  • C. Kipnis and S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Commun. Math. Phys. 104 (1986), pp. 1–19.
  • J. Lőrinczi, F. Hiroshima, and V. Betz, Feynman-Kac-type Theorems and Gibbs Measures on Path Space with Applications to Rigorous Quantum Field Theory. Walter de Gruyter, Berlin, 2011.
  • N. Obata, White Noise Calculus and Fock space, Lecture Notes in Mathematics Vol. 1577, Springer, Berlin, 1994.
  • H. Spohn, Ground state(s) of the spin-boson Hamiltonian, Commun. Math. Phys. 123 (1989), pp. 277–304.

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