The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field
發表於2024-11-09
Topics in Random Matrix Theory 2024 pdf epub mobi 電子書 下載
圖書標籤: 數學 Mathematics 隨機矩陣 其餘代數7 Stochastics Statistics Probability Math
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評分Tao寫書真的太清楚瞭
評分Tao的風格很明顯,偏重組閤,概率味道反而不夠,基本就是為瞭證明圓律做準備的。RMT裏其他重要內容,像Tracy-Widom distribution都沒提也是很神奇。而且寫作順序上,開頭花瞭兩章來敘述concentration measures和CLT證明的技術,導緻講semi circle law和circular law的時候要不停地引好幾章之前的結論,看起來非常麻煩。還是看AGZ的好。
Topics in Random Matrix Theory 2024 pdf epub mobi 電子書 下載