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1	Gap Probabilities in Random Matrix Ensembles Bäcklin, Oskar January 2023 (has links) In this degree project we look at eigenvalue statistics of two randommatrix ensembles, the Gaussian and the circular ensembles. We beginwith their definition and discuss the joint probability distribution of theirentries and eigenvalues. In addition we introduce two sparse matrix models which enables us to numerically compute some eigenvalues statisticsfor these ensembles via the use of simulation. In particular we focus on thegap probability. Lastly we present and discuss the result of the numerical simulations. gap probability random matrix Mathematics Matematik Probability Theory and Statistics Sannolikhetsteori och statistik
2	Topics in random matrices and statistical machine learning / ランダム行列と統計的機械学習について Sushma, Kumari 25 September 2018 (has links) 京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21327号 / 理博第4423号 / 新制\|\|理\|\|1635(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 COLLINS,Benoit Vincent Pierre, 教授泉正己, 教授日野正訓 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM Wishart matrices $(m, n, beta)$-Laguerre matrices compound Wishart matrices joint eigenvalue density gap probability inverse moments finiteness condition $k$-nearest neighbor rule Stone`s theorem metrically sigma-finite dimensional space Nagata dimension generalized Stone`s lemma, Preiss` result weak and strong consistency 400

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Gap Probabilities in Random Matrix Ensembles

Topics in random matrices and statistical machine learning / ランダム行列と統計的機械学習について