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The EM Algorithm applied to determining new limit points of Mahler measures

El Otmani S., Rhin G., Sac-Epee J. M.

Control and Cybernetics

2010

Vol. 39, no 4

1185-1192

In this work, we propose new candidates expected to be limit points of Mahler measures of polynomials. The tool we use for determining these candidates is the Expectation-Maximization algorithm, whose goal is to optimize the likelihood for the given data points, i.e. the known Mahler measures up to degree 44, to be generated by a specific mixture of Gaussians. We will give the mean (which is a candidate to be a new limit point) and the relative amplitude of each component of the more likely gaussian mixture.