Fluctuations in the half-heavy tailed Wigner ensemble (Mathematical Physics Seminar)

Mathematical Physics Seminar

Speaker: Anna Maltsev, University of Bristol
http://www.bristol.ac.uk/maths/people/anna-v-maltsev/overview.html

Fluctuations in the half-heavy tailed Wigner ensemble
We will consider a Wigner matrix with entries whose cumulative
distribution decays as $x^{-\alpha}$ with $2<\alpha<4$ for large $x$.
We prove that the fluctuations of the linear spectral statistics for
nice test functions have order $N^{-\alpha/4}$. The behavior of such
fluctuations has been understood for both heavy-tailed matrices (i.e.
$\alpha < 2$) and light-tailed matrices (i.e. $\alpha > 4$). Our
result fills in the gap of understanding for $2 < \alpha < 4$.