Showing papers on "Gaussian measure published in 1982"
Journal Article•
TL;DR: In this paper, the authors proposed a method to solve the problem of the lack of resources in the field of computer science and applied it to computer graphics design, including the following:
Abstract: 報告番号: 乙05942 ; 学位授与年月日: 1982-02-08 ; 学位の種別: 論文博士 ; 学位の種類: 理学博士 ; 学位記番号: 第5942号 ; 研究科・専攻: 理学系研究科
115 citations
TL;DR: For a new class of Gaussian function space integrals, the exponential rate of growth or decay as $n \rightarrow \infty$ is determined in this article, where the results are applied to the calculation of specific free energy in statistical mechanics.
Abstract: For a new class of Gaussian function space integrals depending upon $n \in \{1, 2,\cdots\}$, the exponential rate of growth or decay as $n \rightarrow \infty$ is determined. The result is applied to the calculation of the specific free energy in a model in statistical mechanics. The physical discussion is self-contained. The paper ends by proving upper bounds on certain probabilities. These bounds will be used in a sequel to this paper, in which asymptotic expansions and limit theorems will be proved for the Gaussian integrals considered here.
48 citations
CERN1
TL;DR: In this article, the SU(N) lattice gauge theories are reformulated in terms of fields varying over non-compact spaces, transforming as N dimensional representations of SU(n) and integrated with Gaussian measure.
Abstract: SU(N) lattice gauge theories are reformulated in terms of fields varying over non-compact spaces ℂ
N
, transforming asN dimensional representations of SU(N) and integrated with Gaussian measure. This reformulation is equivalent to a boson operator representation. Strong coupling expansions based on this formalism do not involve SU(N) vector coupling coefficients.
3 citations
01 Jan 1982
TL;DR: In this paper, weak convergence of Gaussian measures and Gaussian transforms is discussed. And the authors present the unique divisibility of infinitely divisible σ-smooth measures on R ( k ).
Abstract: This chapter discusses weak convergence on R ( k ) . It presents Gaussian measures and Gaussian transforms. The chapter also discusses fourier transforms and their relation to Gaussian transforms. It presents the unique divisibility of infinitely divisible σ-smooth measures. A σ-smooth infinitely divisible measure on R ( k ) is uniquely infinitely divisible. A sequence { μ n } of Gaussian measures converges weakly and then to a Gaussian measure if and only if the sequence of the mean-value vectors of μ n and the sequence of moment matrices converge to a moment vector and a moment matrix belonging to a Gaussian measure.
3 citations
01 Jan 1982
TL;DR: In this paper, it was shown that a Gaussian measure induces a Kubo-Martin-Schwinger state for the linear system, and that the preimage of this measure under the canonical transformation implemented by a wave operator is a KMLS state.
Abstract: A smoothed nonlinear Klein-Gordon equation is regarded as the equation of evolution of a classical dynamical system with an infinite-dimensional phase space. It is proved that the wave operators are canonical transformations of this system that linearize it. It is shown that a Gaussian measure induces a Kubo-Martin-Schwinger state for the linear system, and that the preimage of this measure under the canonical transformation implemented by a wave operator is a Kubo-Martin-Schwinger state for the original nonlinear system.Bibliography: 8 titles.
01 Apr 1982
TL;DR: In this article, it was shown that the orthogonal series I' I a, ("x)x, converges in SC,-almost everywhere and it holds that x = a,"(x,x), "x", "x")x, "x", "u", "u" converges almost everywhere, where H is the generating Hilbert space of,u.
Abstract: Let SC be a separable Hilbert space and ,u a probability Radon measure on SC of second order. Then there exist (a,,) E 12, an O.N.S. (x,,) C SC and an O.N.S. (4,1) C H such that the orthogonal series I' I a,"("x)x, converges in SC ,-almost everywhere and it holds that x = a,"("x)x", ,u-almost everywhere, where H is the generating Hilbert space of ,u. In the case where ,u is a Gaussian measure, a similar result was proved by Kuelbs [2] in general Banach spaces. 1. Let SC be a separable (real or complex) Hilbert space and y a probability measure on SC of second order, that is, X3c x 112 dti(x) < +oo. SC' denotes the dual space of SC and is identified with SC by the conjugate linear isometry X3 3 x ( I x) E SC', where ( I ) is the inner product of SC (Riesz's theorem). Let R: SC' -L2(I) be R(y) = ( I y). We let H be the L2(L)-closure of RX'. Then R: 'JC' -H is a continuous (conjugate) linear mapping since II R(y)112 = I (x |y) 12 dML(x) < (f11X 11 2d,(x)) 11 y 11 2. THEOREM. There exist (an) E 12, an O.N.S. (Xn) C SC and an O.N.S. ((n) C H such that