{"doi":"10.3150/14-BEJ615","year":"2015","external_id":{"arxiv":["1208.5823"],"isi":["000356993100012"]},"publist_id":"5671","issue":"3","status":"public","quality_controlled":"1","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:52:25Z","abstract":[{"lang":"eng","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)."}],"intvolume":"        21","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"LaEr"}],"type":"journal_article","oa":1,"page":"1600 - 1628","publisher":"Bernoulli Society for Mathematical Statistics and Probability","month":"08","_id":"1506","date_updated":"2025-09-23T13:59:56Z","article_processing_charge":"No","isi":1,"title":"The logarithmic law of random determinant","publication":"Bernoulli","author":[{"last_name":"Bao","first_name":"Zhigang","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475"},{"last_name":"Pan","full_name":"Pan, Guangming","first_name":"Guangming"},{"last_name":"Zhou","first_name":"Wang","full_name":"Zhou, Wang"}],"day":"01","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1208.5823"}],"publication_status":"published","arxiv":1,"citation":{"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>","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>.","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>","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.","short":"Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.","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>.","ista":"Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli. 21(3), 1600–1628."},"volume":21,"date_published":"2015-08-01T00:00:00Z"}