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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tracy–Widom distribution ： ウィキペディア英語版 Tracy–Widom distribution The Tracy–Widom distribution, introduced by , is the probability distribution of the normalized largest eigenvalue of a random Hermitian matrix.〔Dominici, D. (2008) ''Special Functions and Orthogonal Polynomials'' American Math. Soc.〕 In practical terms, Tracy-Widom is the crossover function between the two phases of weakly versus strongly coupled components in a system.〔(''Mysterious Statistical Law May Finally Have an Explanation'' ), wired.com 2014-10-27〕 It also appears in the distribution of the length of the longest increasing subsequence of random permutations , in current fluctuations of the asymmetric simple exclusion process (ASEP) with step initial condition (, ), and in simplified mathematical models of the behavior of the longest common subsequence problem on random inputs . See (, ) for experimental testing (and verifying) that the interface fluctuations of a growing droplet (or substrate) are described by the TW distribution $F\_2$ (or $F\_1$) as predicted by (). The distribution ''F''1 is of particular interest in multivariate statistics . For a discussion of the universality of ''F''''β'', ''β'' = 1, 2, and 4, see . For an application of ''F''1 to inferring population structure from genetic data see . ==Definition== The Tracy-Widom distribution is defined as the limit: :$F\_2(s)\; =\; \backslash lim\backslash limits\_\backslash left((\backslash lambda\_-\backslash sqrt)(\backslash sqrt)n^\backslash leq\; s\backslash right)$, The shift by $\backslash sqrt$ is used to keep the distributions centered at 0. The multiplication by $(\backslash sqrt)n^$ is used because the standard deviation of the distributions scales as $n^$. 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「Tracy–Widom distribution」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.