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 xα with 2<α<4 for large x.
We prove that the fluctuations of the linear spectral statistics for
nice test functions have order Nα/4. The behavior of such
fluctuations has been understood for both heavy-tailed matrices (i.e.
α<2) and light-tailed matrices (i.e. α>4). Our
result fills in the gap of understanding for 2<α<4.