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Real moments of the logarithmic derivative of characteristic polynomials in random matrix ensembles

Autor: Ge, Fan

We prove asymptotics for real moments of the logarithmic derivative of characteristic polynomials evaluated at $1-\frac{a}{N}$ in unitary, even orthogonal, and symplectic ensembles, where $a>0$ and $a=o(1)$ as the size $N$ of the matrix goes to infin

Externí odkaz: http://arxiv.org/abs/2304.02153

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Akademický článek

Assessing the ChatGPT aptitude: A competent and effective Dermatology doctor?

Autor: Chengxiang Lian, Xin Yuan, Santosh Chokkakula, Guanqing Wang, Biao Song, Zhe Wang, Ge Fan, Chengliang Yin

Publikováno v: Heliyon, Vol 10, Iss 17, Pp e37220- (2024)

Background: The efficacy and adeptness of ChatGPT 3.5 and ChatGPT 4.0 in the precise diagnosis and management of conditions like atopic dermatitis and Autoimmune blistering skin diseases (AIBD) remain to be elucidated. So this study examined the accu

Externí odkaz: https://doaj.org/article/5d6185c150264da883fdbf172b050524

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On the logarithmic derivative of characteristic polynomials for random unitary matrices

Autor: Ge, Fan

Let $U\in U(N)$ be a random unitary matrix of size $N$, distributed with respect to the Haar measure on $U(N)$. Let $P(z)=P_U(z)$ be the characteristic polynomial of $U$. We prove that for $z$ close to the unit circle, $ \frac{P'}{P}(z) $ can be appr

Externí odkaz: http://arxiv.org/abs/2211.14625

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Mean values of the logarithmic derivative of the Riemann zeta-function near the critical line

Autor: Ge, Fan

Assume the Riemann Hypothesis and a hypothesis on small gaps between zeta zeros, we prove a conjecture of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith, which states that for any positive integer $K$ and real number $a>0$, \begin{a

Externí odkaz: http://arxiv.org/abs/2211.08571

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