{"quality_controlled":"1","title":"The logarithmic law of random determinant","main_file_link":[{"url":"http://arxiv.org/abs/1208.5823","open_access":"1"}],"intvolume":"        21","citation":{"ieee":"Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,” <i>Bernoulli</i>, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics and Probability, pp. 1600–1628, 2015.","ama":"Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. <i>Bernoulli</i>. 2015;21(3):1600-1628. doi:<a href=\"https://doi.org/10.3150/14-BEJ615\">10.3150/14-BEJ615</a>","mla":"Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>, vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability, 2015, pp. 1600–28, doi:<a href=\"https://doi.org/10.3150/14-BEJ615\">10.3150/14-BEJ615</a>.","short":"Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.","apa":"Bao, Z., Pan, G., &#38; Zhou, W. (2015). The logarithmic law of random determinant. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/14-BEJ615\">https://doi.org/10.3150/14-BEJ615</a>","ista":"Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli. 21(3), 1600–1628.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2015. <a href=\"https://doi.org/10.3150/14-BEJ615\">https://doi.org/10.3150/14-BEJ615</a>."},"date_published":"2015-08-01T00:00:00Z","month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","publisher":"Bernoulli Society for Mathematical Statistics and Probability","day":"01","department":[{"_id":"LaEr"}],"date_created":"2018-12-11T11:52:25Z","status":"public","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pan, Guangming","last_name":"Pan","first_name":"Guangming"},{"first_name":"Wang","last_name":"Zhou","full_name":"Zhou, Wang"}],"oa_version":"Preprint","publist_id":"5671","date_updated":"2021-01-12T06:51:14Z","volume":21,"abstract":[{"text":"Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij &lt;∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).","lang":"eng"}],"oa":1,"_id":"1506","type":"journal_article","doi":"10.3150/14-BEJ615","page":"1600 - 1628","issue":"3","publication_status":"published","publication":"Bernoulli","language":[{"iso":"eng"}]}