Oliver Russell

most citedUsing Sums-of-Squares to Prove Gaussian Product Inequalities

4 citations · 8 across the 4 of their papers we have counts for

collaborators

4 papers

math.PR2022★ 3 cited

Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality

Oliver Russell, Wei Sun

We prove the three-dimensional Gaussian product inequality (GPI) $E [X_{1}^{2} X_{2}^{2 m_{2}} X_{3}^{2 m_{3}}] \geq E [X_{1}^{2}] E [X_{2}^{2 m_{2}}] E [X_{3}^{2 m_{3}}]$ for any centered Gaussian random vector $(…

math.PR2022★ 1 cited

An Opposite Gaussian Product Inequality

Oliver Russell, Wei Sun

The long-standing Gaussian product inequality (GPI) conjecture states that $E [\prod_{j = 1}^{n} ∣ X_{j} ∣^{α_{j}}] \geq \prod_{j = 1}^{n} E [∣ X_{j} ∣^{α_{j}}]$ for any centered Gaussian random vector…

math.PR2022★ 4 cited

Using Sums-of-Squares to Prove Gaussian Product Inequalities

Oliver Russell, Wei Sun

The long-standing Gaussian product inequality (GPI) conjecture states that $E [\prod_{j = 1}^{n} X_{j}^{2 m_{j}}] \geq \prod_{j = 1}^{n} E [X_{j}^{2 m_{j}}]$ for any centered Gaussian random vector $…

math.PR2022

Some New Gaussian Product Inequalities

Oliver Russell, Wei Sun

The Gaussian product inequality is a long-standing conjecture. In this paper, we investigate the three-dimensional inequality $E[X_1^{2}X_2^{2m_2}X_3^{2m_3}]\ge E[X_1^{2}]E[X_2^{2m…