The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase
نویسندگان
چکیده
منابع مشابه
On the Characteristic Polynomial of a Random Unitary Matrix
We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N ×N unitary matrix, as N → ∞. First we show that lnZ/ √ 1 2 lnN , evaluated at a finite set of distinct points, is asymptotically a collection of i.i.d. complex normal random variables. This leads to a refinement of a recent central limit theorem due to Keating and Sn...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2015
ISSN: 1083-6489
DOI: 10.1214/ejp.v20-4296