Transcendence of logarithmic Voronoi cells for unrestricted correlation models

Determine whether logarithmic Voronoi cells of unrestricted correlation models are transcendental, as conjectured in the Gaussian analogue of logarithmic Voronoi theory.

Background

The paper situates its results within prior work on Gaussian analogues of logarithmic Voronoi cells. In that setting, the cells for the bivariate correlation model were shown to be semialgebraic, while the corresponding algebraic or transcendental nature of cells for unrestricted correlation models was not resolved and was instead stated as a conjecture. The present paper establishes transcendence phenomena for one-dimensional algebraic statistical models, but it does not settle the cited conjecture for unrestricted correlation models.

References

In that setting, the cells of the bivariate correlation model were shown to be semialgebraic, whereas those of unrestricted correlation models were conjectured to be transcendental.

— Boundaries of logarithmic Voronoi cells can be transcendental  (2608.18434 - Alexandr, 19 Aug 2026) in Introduction, paragraph beginning “Logarithmic Voronoi cells were introduced…”