{"ID":3052299,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-06T04:39:12.706778348Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04440","arxiv_id":"2606.04440","title":"Asymptotic analysis of parameterised univariate Gaussian splitting","abstract":"This document provides in-depth details for the derivation of the univariate splitting algorithm developed in arXiv:2606.01530. The algorithm approximates the standard, 1-D Gaussian distribution with a mixture of uniformly spaced homoscedastic Gaussian components. The solution is found by minimising the squared $L^2$ norm of the mismatch between the approximation and the original Gaussian. This text presents asymptotic analyses of the proposed splitting in the limit of small step $h$ between the mixand means and in the limit of large number of mixands $M$.","short_abstract":"This document provides in-depth details for the derivation of the univariate splitting algorithm developed in arXiv:2606.01530. The algorithm approximates the standard, 1-D Gaussian distribution with a mixture of uniformly spaced homoscedastic Gaussian components. The solution is found by minimising the squared $L^2$ n...","url_abs":"https://arxiv.org/abs/2606.04440","url_pdf":"https://arxiv.org/pdf/2606.04440v1","authors":"[\"Dmitry Mikhin\",\"Athena Xiourouppa\"]","published":"2026-06-03T04:41:29Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}