翻訳と辞書 Words near each other ・ Laplace expansion ・ Laplace expansion (potential) ・ Laplace formula ・ Laplace functional ・ Laplace invariant ・ Laplace Island ・ Laplace Island (Antarctica) ・ Laplace Island (Western Australia) ・ Laplace limit ・ Laplace no Ma ・ Laplace number ・ Laplace operator ・ Laplace operators in differential geometry ・ Laplace plane ・ Laplace pressure ・ Laplace principle (large deviations theory) ・ Laplace transform ・ Laplace transform applied to differential equations ・ Laplace's demon ・ Laplace's equation ・ Laplace's law ・ Laplace's method ・ LaPlace, Louisiana ・ Laplace-P ・ LaplacesDemon ・ Laplace–Beltrami operator ・ Laplace–Carson transform ・ Laplace–Runge–Lenz vector ・ Laplace–Stieltjes transform ・ Laplacian matrix Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Laplace principle (large deviations theory) ： ウィキペディア英語版 Laplace principle (large deviations theory) In mathematics, Laplace's principle is a basic theorem in large deviations theory, similar to Varadhan's lemma. It gives an asymptotic expression for the Lebesgue integral of exp(−''θφ''(''x'')) over a fixed set ''A'' as ''θ'' becomes large. Such expressions can be used, for example, in statistical mechanics to determining the limiting behaviour of a system as the temperature tends to absolute zero. ==Statement of the result== Let ''A'' be a Lebesgue-measurable subset of ''d''-dimensional Euclidean space R''d'' and let ''φ'' : R''d'' → R be a measurable function with : Then :$\backslash lim\_\; \backslash frac1\; \backslash log\; \backslash int\_\; e^\; \backslash ,\; \backslash mathrm\; x\; =\; -\; \backslash mathop\; \backslash varphi(x),$ where ess inf denotes the essential infimum. Heuristically, this may be read as saying that for large ''θ'', :$\backslash int\_\; e^\; \backslash ,\; \backslash mathrm\; x\; \backslash approx\; \backslash exp\; \backslash left(\; -\; \backslash theta\; \backslash mathop\; \backslash varphi(x)\; \backslash right).$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Laplace principle (large deviations theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.