147 citations · 236 across the 17 of their papers we have counts for
18 papers
Non-Archimedean Electrostatics
Christopher D. Sinclair
We introduce ensembles of repelling charged particles restricted to a ball in a non-archimedean field (such as the -adic numbers) with interaction energy between pairs of partic…
The reciprocal Mahler ensembles of random polynomials
Christopher D. Sinclair, Maxim L. Yattselev
We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree whose Mahler measure is bounded by a constant. After a change of variables this redu…
A Solvable Two-Charge Ensemble on the Circle
Christopher Shum, Christopher D. Sinclair
We introduce an ensemble consisting of logarithmically repelling charge one and charge two particles on the unit circle constrained so that the total charge of all particles equals…
Equidistribution of Elements of Norm 1 in Cyclic Extensions
Kathleen L. Petersen, Christopher D. Sinclair
Upon quotienting by units, the elements of norm 1 in a number field form a countable subset of a torus of dimension where and are the numbers of rea…
Root Statistics of Random Polynomials with Bounded Mahler Measure
Christopher D. Sinclair, Maxim L. Yattselev
The Mahler measure of a polynomial is a measure of complexity formed by taking the modulus of the leading coefficient times the modulus of the product of its roots outside the unit…
Extremal laws for the real Ginibre ensemble
Brian Rider, Christopher D. Sinclair
The real Ginibre ensemble refers to the family of matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result…