What question did this study set out to answer?

The aim is to prove the Gaussian Moments Conjecture for two real Gaussian variables, identifying conditions on polynomials that affect their moments.

July 26, 2026Open Access

The Gaussian Moments Conjecture in Two Variables

View Full Paper

Ask AI

Bookmark

Authors

This preprint demonstrates the Gaussian Moments Conjecture for two Gaussian variables, indicating specific conditions for moment behavior.

The aim is to prove the Gaussian Moments Conjecture for two real Gaussian variables, identifying conditions on polynomials that affect their moments.
Used circular coordinates to perform Gaussian integration and extract constant terms.
Applied the Duistermaat–van der Kallen constant-term theorem and a reduction-modulo-(p) approach.
Formalized the proof in Lean.
Every polynomial with all positive Gaussian moments equaling zero has rotational weights of one strict sign.
Proves the mixed-moment conclusion for the conjecture in dimension two.
Determines the dimensional range for the Gaussian Moments Conjecture, contrasting with existing counterexamples in higher dimensions.

Roy van Rijn (2026) studied this question.

View Full Paper

Ask AI

Bookmark

This preprint demonstrates the Gaussian Moments Conjecture for two Gaussian variables, indicating specific conditions for moment behavior.