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Asymptotic analysis of Gaussian integrals, II: Manifold of minimum points

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Abstract

This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action form a nondegenerate manifold. Such integrals play an important role in recent physics. This paper also proves limit theorems for related probability measures, analogous to the classical law of large numbers and central limit theorem.

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References

  • Billingsley, P.: Convergence of Probability Measures. New York: John Wiley and Sons 1968

    Google Scholar 

  • Coleman, S.: The Uses of Instantons. Lectures delivered at the 1977 International School of Subnuclear Physics, Ettore Majorana

  • Donsker, M. D., Varadhan, S. R. S.: Commun. Pure Appl. Math.29, 389–461 (1976)

    Google Scholar 

  • Ellis, R. S., Rosen, Jay S.: 1. Asymptotic analysis of Gaussian integrals, I.: isolated minimum points. Trans. Am. Math. Soc. (to appear). 2. Laplace's method for Gaussian integrals with an application to statistical mechanics. Annals of Probab. (to appear)

  • Gihman, I. I., Skorohod, A. V.: The Theory of Stochastic Processes I. Transl. by S. Kotz, Berlin, Heidelberg New York: Springer 1974

    Google Scholar 

  • Guillemin, V., Pollack, A.: Differential topology. Englewood Cliffs, N. J.: Prentice Hall, 1974

    Google Scholar 

  • Jain, N. C., Marcus, M. B.: Continuity of subgaussian processes. Univ. of Minn./Northwestern Univ. Preprint (1978)

  • Marcus, M. B., Shepp, L. A.: Sample behavior of Gaussian processes. In: Sixth Berkeley Symposium on Math. Stat. and Probability, Vol. II, 423–439 (1972)

  • Pincus, M.: Trans. Am. Math. Soc.134, 193–216 (1968)

    Google Scholar 

  • Royden, H. L.: Real analysis. New York: Macmillan 1963

    Google Scholar 

  • Schilder, M.: Trans. Am. Math. Soc.125, 63–85 (1966)

    Google Scholar 

  • Simon, B.: 1. Functional Integration and Quantum Physics. New York: Academic Press 1979. 2. Trace Ideals and Their Applications. Cambridge: Cambridge Univ. Press 1979

    Google Scholar 

  • Spivak, M.: A Comprehensive Introduction to Differential Topology. Vol. I–IV, Berkeley: Publish or Perish 1970

    Google Scholar 

  • Varadhan, S. R. S.: Commun. Pure Appl. Math.19, 261–286 (1966)

    Google Scholar 

  • Weyl, H.: Am. J. Math.61, 461–472 (1939)

    Google Scholar 

  • Wiegel, F. W.: Phys. Rep.16, 57–114 (1975)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, MA, USA

    Richard S. Ellis & Jay S. Rosen

Authors
  1. Richard S. Ellis
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  2. Jay S. Rosen
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Additional information

Communicated by B. Simon

Alfred P. Sloan Research Fellow. Research supported in part by NSF Grant MCS-80-02149

Research supported in part by NSF Grant MCS-80-02140

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Ellis, R.S., Rosen, J.S. Asymptotic analysis of Gaussian integrals, II: Manifold of minimum points. Commun.Math. Phys. 82, 153–181 (1981). https://doi.org/10.1007/BF02099914

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  • DOI: https://doi.org/10.1007/BF02099914

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