{"id":32774,"date":"2018-10-08T00:05:54","date_gmt":"2018-10-07T16:05:54","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=32774"},"modified":"2018-10-08T09:06:19","modified_gmt":"2018-10-08T01:06:19","slug":"%e6%8a%95%e8%b3%87%e5%ad%b8%e3%80%81%e6%a0%b8%e7%89%a9%e7%90%86%e8%88%87%e9%9a%a8%e6%a9%9f%e7%9f%a9%e9%99%a3%ef%bc%88%e4%ba%8c%ef%bc%89","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=32774","title":{"rendered":"\u6295\u8cc7\u5b78\u3001\u6838\u7269\u7406\u8207\u96a8\u6a5f\u77e9\u9663\uff08\u4e8c\uff09"},"content":{"rendered":"<figure id=\"attachment_32775\" aria-describedby=\"caption-attachment-32775\" style=\"width: 450px\" class=\"wp-caption alignleft\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-32775\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/fig0-1.jpg\" alt=\"\" width=\"450\" height=\"312\" data-wp-pid=\"32775\"><figcaption id=\"caption-attachment-32775\" class=\"wp-caption-text\">Figure0. \u6211\u5011\u5c0d\u89d2\u5316\u4e86 100 \u500b 500 * 500 \u7684\u5c0d\u7a31\u77e9\u9663\uff0c\u77e9\u9663\u5143\u7d20\u90fd\u662f\u5e38\u614b\u5206\u4f48 N(0,1)\u96a8\u6a5f\u7522\u751f\u7684\uff0c\u6211\u5011\u5c07\u5149\u8b5c\u7684\u5206\u4f48\u756b\u6210\u76f4\u65b9\u5716\uff0c\u767c\u73fe\u9019\u500b\u5206\u4f48\u5f62\u6210\u4e86\u534a\u5713\u3002<\/figcaption><\/figure>\n<p><strong>\u64b0\u6587\uff5c\u856d\u7dad\u7ff0<\/strong><\/p>\n<p>\u5728<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=32768\" target=\"_blank\" rel=\"noopener noreferrer\">\u524d\u6587\u4e2d<\/a>\u7b46\u8005\u5617\u8a66\u8aaa\u670d\u8b80\u8005\uff0c\u6295\u8cc7\u7684\u7b56\u7565\u662f\u53ef\u4ee5\u5229\u7528\u6578\u5b78\u53bb\u512a\u5316\u7684\u3002\u4f46\u5373\u4fbf\u53ea\u91dd\u5c0d\u96a8\u6a5f\u904e\u7a0b\uff0c\u4f9d\u820a\u6709\u592a\u591a\u5de5\u5177\u53ef\u4ee5\u9078\u64c7\u3002\u672c\u7cfb\u5217\u6587\u5c07\u5074\u91cd\u65bc\u96a8\u6a5f\u77e9\u9663\u9019\u500b\u4f8b\u5b50\uff0c\u65e5\u5f8c\u6709\u6a5f\u6703\u518d\u804a\u804a\u5176\u4ed6\u7684\u5de5\u5177\u3002\u800c\u9078\u64c7\u96a8\u6a5f\u77e9\u9663\u7684\u539f\u56e0\u4e43\u5728\u65bc\u9019\u500b\u6578\u5b78\u5206\u652f\u4e00\u90e8\u5206\u7684\u91cd\u8981\u8ca2\u737b\u4f86\u81ea\u65bc\u6838\u7269\u7406\u7684\u7814\u7a76\u3002<\/p>\n<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u5011\u5c07\u56de\u9867\u96a8\u6a5f\u77e9\u9663\u5728\u6838\u7269\u7406\u767c\u5c55\u4e2d\u7522\u751f\u7684\u52a9\u529b\uff0c\u4e26\u5728\u4e0b\u7bc7\u62c9\u56de\u8fd1\u4ee3\uff0c\u8aaa\u660e\u9019\u4e9b\u60f3\u6cd5\u600e\u9ebc\u88ab\u4f7f\u7528\u5230\u8ca1\u52d9\u554f\u984c\u4e2d\u3002<\/p>\n<p>\u6642\u9593\u62c9\u56de\u5230 1950 \u5e74\u4ee3\uff0c\u7269\u7406\u5b78\u5bb6\u5011\u5728\u6838\u7269\u7406\u7684\u5be6\u9a57\u4e2d\u89c0\u5bdf\u5230\u8a31\u591a\u5149\u8b5c\u7dda\u3002\u9019\u88e1\u7684\u5149\u8b5c\u7dda\u7684\u6982\u5ff5\u548c\u9ad8\u4e2d\u5316\u5b78\u7684\u6c2b\u539f\u5b50\u5149\u8b5c\u662f\u4e00\u6a23\u7684\u3002\u7c21\u800c\u8a00\u4e4b\uff0c\u859b\u4e01\u683c\u65b9\u7a0b\u5f0f\u6703\u6c7a\u5b9a\u4e00\u500b\u7cfb\u7d71\uff08\u6bd4\u5982\u8aaa\u6c2b\u539f\u5b50\uff09\u5141\u8a31\u5177\u5099\u7684\u7a69\u5b9a\u72c0\u614b\u8207\u9019\u500b\u72c0\u614b\u5177\u5099\u7684\u80fd\u91cf\u6709\u54ea\u4e9b\uff0c\u7576\u7cfb\u7d71\u5f9e\u4e00\u500b\u72c0\u614b\u8df3\u5230\u53e6\u4e00\u500b\u72c0\u614b\uff0c\u5169\u72c0\u614b\u4e4b\u9593\u7684\u80fd\u91cf\u5dee\u4ee5\u96fb\u78c1\u6ce2\u7684\u65b9\u5f0f\u91cb\u653e\u4e26\u88ab\u5be6\u9a57\u89c0\u5bdf\u5230\uff0c\u4fbf\u662f\u5149\u8b5c\u3002<\/p>\n<p>\u5be6\u9a57\u4e0a\uff0c\u5c0d\u65bc\u5149\u8b5c\u7684\u4e86\u89e3\u6709\u52a9\u65bc\u6211\u5011\u56de\u63a8\u4e00\u500b\u7cfb\u7d71\u53ef\u80fd\u5177\u5099\u7684\u7d50\u69cb\u3002\uff08\u8b6c\u5982\u7576\u521d\u5e96\u7acb\uff08W. 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<em>E<\/em> \u7684\u5730\u65b9\u6709\u4e00\u689d\u5149\u8b5c\u7dda\uff0c\u90a3\u9ebc\u8ddd\u96e2\u9019\u500b\u9ede <em>S<\/em> \u55ae\u4f4d\u80fd\u91cf\u5167\u90fd\u6c92\u6709\u53e6\u5916\u4e00\u689d\u5149\u8b5c\u7dda\u7684\u6a5f\u7387 \u662f\u591a\u5c11\uff1f<\/p>\n<p>\u5018\u82e5\u6211\u5011\u5047\u8a2d\u4e0d\u540c\u80fd\u968e\u4e4b\u9593\u662f\u6c92\u6709\u7d71\u8a08\u4e0a\u7684\u95dc\u806f\u7684\uff0c\u90a3\u9ebc\u6709\u4e0a\u904e\u4e09\u985e\u7d44\u7684\u5927\u4e00\u5fae\u7a4d\u5206\uff08\u6216\u4e0d\u5c0f\u5fc3\u5b78\u4e86\u5927\u5b78\u90e8\u7684\u6a5f\u7387\u8207\u7d71\u8a08\uff09\u7684\u8b80\u8005\u5011\u6703\u767c\u73fe\u9019\u662f\u500b Poisson 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\u904e\u7a0b\u7684\u89e3\u62ff\u53bb\u8207\u5be6\u9a57\u7d71\u8a08\u7684\u6578\u5b57\u6bd4\u5c0d\uff0c\u5be6\u5728\u76f8\u53bb\u751a\u9060\u3002\u4f46\u81f3\u5c11\u6211\u5011\u5f9e\u4e2d\u5f97\u5230\u4e86\u4e00\u500b\u7d50\u8ad6\uff1a\u81f3\u5c11\u5728\u5177\u6709\u76f8\u540c\u91cf\u5b50\u6578\u7684\u90a3\u5806\u80fd\u968e\u9593\uff0c\u5b83\u5011\u662f\u6709\u7d71\u8a08\u95dc\u806f\u7684\uff0c\u90a3\u9ebc\u4e0b\u4e00\u500b\u554f\u984c\u5c31\u662f\uff0c\u6709\u6c92\u6709\u4e00\u500b\u7c21\u55ae\u597d\u61c2\u7684\u6a21\u578b\u8b93\u6211\u5011\u61c2\u9019\u500b\u95dc\u806f\uff1f<\/p>\n<p>\u7b46\u8005\u6240\u77e5\u9053\u6700\u7c21\u55ae\u7684\u4f8b\u5b50\u662f\u6240\u8b02\u7684\u9ad8\u65af\u7cfb\u7d9c\uff08Gaussian ensemble\uff09\uff0c\u800c\u5728\u8af8\u591a\u9ad8\u65af\u7cfb\u7d9c\u4e2d\uff0c\u6700\u7c21\u55ae\u7684\u4f8b\u5b50\u662f\u9ad8\u65af\u6b63\u4ea4\u7cfb\u7d9c\uff08Gaussian orthogonal ensemble\uff0cGOE\uff09\u3002\u8b80\u8005\u5b8c\u5168\u4e0d\u7528\u53bb\u8ffd\u7a76\u9019\u4e9b\u55ae\u5b57\u7684\u610f\u601d\uff0c\u9019\u985e\u77e9\u9663\u7684\u610f\u601d\u662f\uff0c\u6709\u4e00\u5806\u5be6\u6578\u5c0d\u7a31\u77e9\u9663\uff0c\u5b83\u5011\u7684\u77e9\u9663\u5143\u7d20\u7531\u5e38\u614b\u5206\u4f48\u7d66\u51fa\u3002\u5be6\u6578\u3001\u5c0d\u7a31\u77e9\u9663\u3001\u8ddf\u5e38\u614b\u5206\u4f48\uff0c\u6574\u500b\u96e3\u5ea6\u4e00\u4e0b\u56de\u5230\u4e86\u9ad8\u4e09\u6578\u5b78\u3002\u50c5\u50c5\u5206\u6790\u9019\u985e\u77e9\u9663\u7684\u80fd\u8b5c\u5c31\u9084\u6eff\u6709\u8da3\u7684\uff0c\u8b6c\u5982\u5b83\u5011\u7684\u80fd\u8b5c\u5206\u4f48\u6703\u88ab\u4fb7\u9650\u5728\u4e00\u500b\u534a\u5713\u4e4b\u4e2d\uff08\u898b\u5716\u96f6\uff09\uff0c\u9019\u4e5f\u662f\u6709\u540d\u7684\u534a\u5713\u5f8b\uff08semi-circle law\uff09\u3002<\/p>\n<figure id=\"attachment_32776\" aria-describedby=\"caption-attachment-32776\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-32776\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/figure1.jpg\" alt=\"\" width=\"650\" height=\"457\" data-wp-pid=\"32776\"><figcaption id=\"caption-attachment-32776\" class=\"wp-caption-text\">Figure1. \u82e5\u80fd\u968e\u4e4b\u9593\u6c92\u6709\u7d71\u8a08\u95dc\u806f\u800c\u9075\u5b88 Poisson \u5206\u4f48\uff0c\u5149\u8b5c\u7dda\u9593\u7684\u8ddd\u96e2\u61c9\u6709\u7684\u5206\u4f48\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u651d\uff09<\/figcaption><\/figure>\n<p>1951 \u5e74\uff0c\u900f\u904e\u5c0d\u5e7e\u500b\u7c21\u55ae\u7684\u9ad8\u65af\u7cfb\u7d9c\u7684\u8a08\u7b97\uff0c\u7269\u7406\u5b78\u5bb6 E. Wigner \u63d0\u51fa\u4e86\u8457\u540d\u7684 Wigner surmise \uff0c\u4e26\u63a8\u6e2c\u4e86\u524d\u8ff0\u7684 &nbsp;\u61c9\u8a72\u6709\u7684\u5f62\u5f0f\u2014 \u4e26\u4e0d\u662f Poisson \u904e\u7a0b\uff0c\u800c\u662f\u5982\u5716\u4e8c\u6240\u793a\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u9019\u500b\u65b0\u7684\u5206\u4f48\u5728\u539f\u9ede\u70ba\u96f6\uff1a \uff0c\u610f\u6307\u4e86\u5169\u500b\u80fd\u968e\u9593\u6703\u907f\u514d\u4ea4\u6703\uff0c\u9019\u7a2e\u73fe\u8c61\u662f\u91cf\u5b50\u7cfb\u7d71\u7684\u4e00\u500b\u7279\u5fb5\u3002<\/p>\n<p>\u8fd1 70 \u5e74\u5f8c\u7684\u4eca\u65e5\u56de\u9867\u9019\u6bb5\u6b77\u53f2\u5176\u5be6\u9084\u9817\u6709\u8da3\u7684\u3002\u7531\u5f8c\u4f86\u7684\u7d71\u8a08\u5206\u6790\uff0c\u6211\u5011\u5f97\u77e5\u6c92\u6709\u4efb\u4f55\u4e00\u7a2e\u9ad8\u65af\u7cfb\u7d9c\u53ef\u4ee5\u5b8c\u7f8e\u7b26\u5408\u6838\u7269\u7406\u5149\u8b5c\u7684\u80fd\u9699\u5206\u4f48\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u7576\u6211\u5011\u771f\u7684\u7528\u9ad8\u65af\u6b63\u4ea4\u7cfb\u7d9c\u9032\u884c\u8a08\u7b97\uff0cWigner surmise \u4e5f\u53ea\u6e96\u78ba\u5230\u5927\u6982 95% \u7684\u7a0b\u5ea6\u3002\uff08\u4e0d\u904e\u4ee5\u731c\u7b54\u6848\u7684\u89c0\u9ede\u4f86\u8aaa\uff0c\u5728\u5b9a\u91cf\u4e0a\u9019\u5df2\u7d93\u6e96\u78ba\u5f97\u99ed\u4eba\u4e86\u3002\uff09 \u7136\u800c\u9019\u4e9b\u7814\u7a76\u5728\u96a8\u6a5f\u77e9\u9663\u7684\u767c\u5c55\u4f9d\u820a\u8d77\u4e86\u6839\u672c\u6027\u7684\u885d\u64ca\u3002\u7dca\u63a5\u8457\u5728\u4e0b\u4e00\u7bc7\uff0c\u6211\u5c07\u8ddf\u5927\u5bb6\u5206\u4eab\u9019\u7a2e\u5206\u6790\u624b\u6cd5\u5982\u4f55\u88ab\u61c9\u7528\u5728\u77ad\u89e3\u91d1\u878d\u6578\u64da\u7684\u554f\u984c\u4e0a\u3002<\/p>\n<figure id=\"attachment_32777\" aria-describedby=\"caption-attachment-32777\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-32777\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/figure2.jpg\" alt=\"\" width=\"650\" height=\"462\" data-wp-pid=\"32777\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/figure2.jpg 1500w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/figure2-800x569.jpg 800w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-32777\" class=\"wp-caption-text\">Figure2. Wigner surmise \u6240\u63d0\u51fa\u7684\u5149\u8b5c\u7dda\u9593\u8ddd\u7684\u5206\u4f48\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p><strong>\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><br \/>\n[1] M. L. Mehta, Random Matrices (2004).<br \/>\n[2] E. Wigner, Ann. Math. <strong>53<\/strong>, 36 (1951).<br \/>\n[3] E. Wigner, Random Matrices in Physics, SIAM Review, Vol. 9, No. 1 (1967).<br \/>\n[4] T. Guhr, Random Matrix Theory in Physics<\/p>\n<p>&nbsp;<\/p>\n<p><strong>--<br \/>\n\u4f5c\u8005\uff1a\u856d\u7dad\u7ff0\uff0c\u81fa\u5927\u7269\u7406\u7cfb\u7562\u696d\u5f8c\u9003\u5230\u829d\u52a0\u54e5\uff0c\u5439\u98a8\u5439\u96ea\u4e4b\u9918\uff0c\u505a\u7814\u7a76\u8b80\u535a\u58eb\u73ed\u3002\u53ef\u60dc\u96e2\u958b\u81fa\u7063\u5f8c\u7121\u6d77\u53ef\u770b\uff0c\u53ea\u80fd\u5728\u5bc6\u897f\u6839\u6e56\u65c1\u63c0\u4e00\u65b9\u5824\u5cb8\uff0c\u507d\u88dd\u6210\u770b\u6d77\u7684\u4eba\u3002\u79d1\u6559\u4e2d\u5fc3\u7279\u7d04\u5beb\u624b\uff0c\u5f9e\u4e8b\u79d1\u666e\u6587\u7ae0\u5beb\u4f5c\u3002<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0\u6642\u9593\u62c9\u56de\u5230 1950 \u5e74\u4ee3\uff0c\u7269\u7406\u5b78\u5bb6\u5011\u5728\u6838\u7269\u7406\u7684\u5be6\u9a57\u4e2d\u89c0\u5bdf\u5230\u8a31\u591a\u5149\u8b5c\u7dda\u3002\u9019\u88e1\u7684\u5149\u8b5c\u7dda\u7684\u6982\u5ff5\u548c\u9ad8\u4e2d\u5316\u5b78\u7684\u6c2b\u539f\u5b50\u5149\u8b5c\u662f\u4e00\u6a23\u7684\u3002\u7c21\u800c\u8a00\u4e4b\uff0c\u859b\u4e01\u683c\u65b9\u7a0b\u5f0f\u6703\u6c7a\u5b9a\u4e00\u500b\u7cfb\u7d71\uff08\u6bd4\u5982\u8aaa\u6c2b\u539f\u5b50\uff09\u5141\u8a31\u5177\u5099\u7684\u7a69\u5b9a\u72c0\u614b\u8207\u9019\u500b\u72c0\u614b\u5177\u5099\u7684\u80fd\u91cf\u6709\u54ea\u4e9b\uff0c\u7576\u7cfb\u7d71\u5f9e\u4e00\u500b\u72c0\u614b\u8df3\u5230\u53e6\u4e00\u500b\u72c0\u614b\uff0c\u5169\u72c0\u614b\u4e4b\u9593\u7684\u80fd\u91cf\u5dee\u4ee5\u96fb\u78c1\u6ce2\u7684\u65b9\u5f0f\u91cb\u653e\u4e26\u88ab\u5be6\u9a57\u89c0\u5bdf\u5230\uff0c\u4fbf\u662f\u5149\u8b5c\u3002<\/p>\n","protected":false},"author":20,"featured_media":32775,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[3964,3960,3963,3962,2487,3965],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/08\/fig0-1.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32774"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32774"}],"version-history":[{"count":2,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32774\/revisions"}],"predecessor-version":[{"id":32780,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32774\/revisions\/32780"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/32775"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32774"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32774"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}