Stephen Willis- Williams College
Stephen Willis
- Williams College
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Introduction
Skills and Expertise
Current institution
Publications
Publications (3)
We study low-lying zeroes of $L$-functions and their $n$-level density, which relies on a smooth test function $\phi$ whose Fourier transform $\widehat\phi$ has compact support. Assuming the generalized Riemann hypothesis, we compute the $n^\text{th}$ centered moments of the $1$-level density of low-lying zeroes of $L$-functions associated with wei...
We introduce a new matrix operation on a pair of matrices, sw(A,X), and discuss its implications on the limiting spectral distribution. In a special case, the resultant ensemble converges almost surely to the Rayleigh distribution. In proving this, we provide a novel combinatorial proof that the random matrix ensemble of circulant Hankel matrices c...
We introduce a new matrix operation on a pair of matrices, $\text{swirl}(A,X),$ and discuss its implications on the limiting spectral distribution. In a special case, the resultant ensemble converges almost surely to the Rayleigh distribution. In proving this, we provide a novel combinatorial proof that the random matrix ensemble of circulant Hanke...
