The reciprocal Mahler ensembles of random polynomials
dc.contributor.author | Sinclair, Christopher D. | |
dc.contributor.author | Yattselev, Maxim L. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2019-08-23T17:33:00Z | |
dc.date.available | 2019-08-23T17:33:00Z | |
dc.date.issued | 2018 | |
dc.description.abstract | We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree N whose Mahler measure is bounded by a constant. After a change of variables, this reduces to a generalization of Ginibre’s complex and real ensembles of random matrices where the weight function (on the eigenvalues of the matrices) is replaced by the exponentiated equilibrium potential of the interval [−2,2] on the real axis in the complex plane. In the complex (real) case, the random roots form a determinantal (Pfaffian) point process, and in both cases, the empirical measure on roots converges weakly to the arcsine distribution supported on [−2,2]. Outside this region, the kernels converge without scaling, implying among other things that there is a positive expected number of outliers away from [−2,2]. These kernels as well as the scaling limits for the kernels in the bulk (−2,2) and at the endpoints {−2,2} are presented. These kernels appear to be new, and we compare their behavior with related kernels which arise from the (non-reciprocal) Mahler measure ensemble of random polynomials as well as the classical Sine and Bessel kernels. | en_US |
dc.eprint.version | Author's manuscript | en_US |
dc.identifier.citation | Sinclair, C. D., & Yattselev, M. L. (2018). The reciprocal Mahler ensembles of random polynomials. Random Matrices: Theory and Applications, 1950012. https://doi.org/10.1142/S2010326319500126 | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/20546 | |
dc.language.iso | en | en_US |
dc.publisher | World Scientific | en_US |
dc.relation.isversionof | 10.1142/S2010326319500126 | en_US |
dc.relation.journal | Random Matrices: Theory and Applications | en_US |
dc.rights | Publisher Policy | en_US |
dc.source | Author | en_US |
dc.subject | Mahler measure | en_US |
dc.subject | random polynomials | en_US |
dc.subject | asymmetric random matrix | en_US |
dc.title | The reciprocal Mahler ensembles of random polynomials | en_US |
dc.type | Article | en_US |