The Alder-Wainwright effect for stationary processes with reflection positivity

Akihiko INOUE

doi:10.2969/jmsj/04330515

Akihiko INOUE

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 3 Pages 515-526

DOI https://doi.org/10.2969/jmsj/04330515

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Published: 1991 Received: January 17, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) B.J. Alder and T.E. Wainwright, Velocity autocorrelations for hard spheres, Phys. Rev. Lett., 18 (1967), 988-990.
2) B.J. Alder and T.E. Wainwright, Decay of the velocity autocorrelation function, Phys. Rev. A, 1 (1970), 18-21.
3) N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular variation, Cambridge University Press, Cambridge, 1987.
4) A. Inoue, The Alder-Wainwright effect for stationary processes with reflection positivity (II), to be submitted in Osaka J. Math..
5) R. Kubo, The fluctuation-dissipation theorem, Rep. Progr. Phys., 29 (1966), 255-284.
6) R. Kubo, Irreversible processes and stochastic processes, Res. Inst. Math. Sci, Kyoto, October, 1979, pp. 50-93 (in Japanese).
7) L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Addison-Wesley, Reading, Massachusetts, 1959.
8) Y. Okabe, On KMO-Langevin equations for stationary Gaussian processes with T-positivity, J. Fac. Sci. Univ. Tokyo, IA 33 (1986), 1-56.
9) Y. Okabe, On the theory of the Brownian motion with the Alder-Wainwright effect, J. Stat. Phys., 45 (1986), 953-981.
10) Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (I), Hokkaido Math. J., 16 (1987), 315-341.
11) Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (II), Hokkaido Math. J., 17 (1988), 1-44.
12) Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (III), Hokkaido Math. J., 18 (1989), 149-174.
13) Y. Okabe, On long time tails of correlation functions for KMO-Langevin equations, Probability Theory and Mathematical Statistics (S. Watanabe and Yu. V. Prokhorov, ed.), Lecture Notes in Math., 1299, Springer, 1988, pp. 391-397.
14) K. Oobayashi, T. Kohno and H. Utiyama, Photon correlation spectroscopy of the non-Markovian Brownian motion of spherical particles, Phys. Rev. A, 27 (1983), 2632-2641.
15) A. Widom, Velocity fluctuation of a hard-core Brownian particle, Phys. Rev. A, 3 (1971), 1394-1396.

Right : [1] B. J. Alder and T. E. Wainwright, Velocity autocorrelations for hard spheres, Phys. Rev. Lett., 18 (1967), 988-990.
[2] B. J. Alder and T. E. Wainwright, Decay of the velocity autocorrelation function, Phys. Rev. A, 1 (1970), 18-21.
[3] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation, Cambridge University Press, Cambridge, 1987.
[4] A. Inoue, The Alder-Wainwright effect for stationary processes with reflection positivity (II), to be submitted in Osaka J. Math..
[5] R. Kubo, The fluctuation-dissipation theorem, Rep. Progr. Phys., 29 (1966), 255-284.
[6] R. Kubo, Irreversible processes and stochastic processes, Res. Inst. Math. Sci, Kyoto, October, 1979, pp. 50-93 (in Japanese).
[7] L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Addison-Wesley, Reading, Massachusetts, 1959.
[8] Y. Okabe, On KMO-Langevin equations for stationary Gaussian processes with T-positivity, J. Fac. Sci. Univ. Tokyo, IA 33 (1986), 1-56.
[9] Y. Okabe, On the theory of the Brownian motion with the Alder-Wainwright effect, J. Stat. Phys., 45 (1986), 953-981.
[10] Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (I), Hokkaido Math. J., 16 (1987), 315-341.
[11] Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (II), Hokkaido Math. J., 17 (1988), 1-44.
[12] Y. Okabe, On the theory of disrete KMO-Langevin equations with reflection positivity (III), Hokkaido Math. J., 18 (1989), 149-174.
[13] Y. Okabe, On long time tails of correlation functions for KMO-Langevin equations, Probability Theory and Mathematical Statistics (S. Watanabe and Yu. V. Prokhorov, ed.), Lecture Notes in Math., 1299, Springer, 1988, pp. 391-397.
[14] K. Oobayashi, T. Kohno and H. Utiyama, Photon correlation spectroscopy of the non-Markovian Brownian motion of spherical particles, Phys. Rev. A, 27 (1983), 2632-2641.
[15] A. Widom, Velocity fluctuation of a hard-core Brownian particle, Phys. Rev. A, 3 (1971), 1394-1396.

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