Proceedings of the Japan Academy, Series A, Mathematical Sciences

Construction of Poissonian Fock space: a simple proof

Yoichiro Takahashi

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Abstract

We introduce an operator which enable us to give a simple construction of the isomorphism from the so-called Fock space to the L2-space with respect to a Poisson measure without combinatorial arguments in Schmidt's orthogonalization procedure.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 86, Number 3 (2010), 60-63.

Dates
First available in Project Euclid: 3 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.pja/1267625641

Digital Object Identifier
doi:10.3792/pjaa.86.60

Mathematical Reviews number (MathSciNet)
MR2650681

Zentralblatt MATH identifier
1196.60090

Subjects
Primary: 60G55: Point processes
Secondary: 60G60: Random fields 82B05: Classical equilibrium statistical mechanics (general)

Keywords
Poisson measure Fock space random point field

Citation

Takahashi, Yoichiro. Construction of Poissonian Fock space: a simple proof. Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 3, 60--63. doi:10.3792/pjaa.86.60. https://projecteuclid.org/euclid.pja/1267625641


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References

  • [SgT]T. Shiga and Y. Takahashi, Ergodic properties of the equilibrium process associated with infinitely many Markovian particles, Publ. Res. Inst. Math. Sci. 9 (1973/74), 505-516.
  • [So]A. Soshnikov, Uspekhi Mat. Nauk 55 (2000), no. 5(335), 107-160; translation in Russian Math. Surveys 55 (2000), no. 5, 923-975.
  • [SrT1]T. Shirai and Y. Takahashi, Fermion process and Fredholm determinant, in Proceedings of the Second ISAAC Congress, Vol. 1 (Fukuoka, 1999), 15-23, Kluwer Acad. Publ., Dordrecht.
  • [SrT2]T. Shirai and Y. Takahashi, Random point fields associated with certain Fredholm determinants. I. Fermion, Poisson and boson point processes, J. Funct. Anal. 205 (2003), no. 2, 414-463.
  • [SrT3]T. Shirai and Y. Takahashi, Random point fields associated with certain Fredholm determinants. II. Fermion shifts and their ergodic and Gibbs properties, Ann. Probab. 31 (2003), no. 3, 1533-1564.
  • [SrT4]T. Shirai and Y. Takahashi, Random point fields associated with fermion, boson and other statistics, in Stochastic analysis on large scale interacting systems, 345-354, Adv. Stud. Pure Math., 39, Math. Soc. Japan, Tokyo.
  • [T1]Y. Takahashi, An integral representation on the path space for scattering length, Osaka J. Math. 27 (1990), no. 2, 373-379.
  • [T2]Y. Takahashi, Absolute continuity of Poisson random fields, Publ. Res. Inst. Math. Sci. 26 (1990), no. 4, 629-647.
  • [T3]Y. Takahashi, Scattering length and large deviation for the symmetric equilibrium process. (in preparation).