There are numerous cases of discrepancies between results obtained in the setting of real
Banach spaces and those obtained in the complex context. This article is a modern …

The Gaussian product inequality is an important conjecture concerning the moments of
Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full …

This note reports partial results related to the Gaussian product inequality (GPI) conjecture
for the joint distribution of traces of Wishart matrices. In particular, several GPI-related results …

The long-standing Gaussian product inequality (GPI) conjecture states that E [∏ j= 1 n| X j| α
j]≥∏ j= 1 n E [| X j| α j] for any centered Gaussian random vector (X 1,…, X n) and any non …

The Gaussian product inequality is a long-standing conjecture. In this paper, we investigate
the three-dimensional inequality E [X 1 2 X 2 2 m 2 X 3 2 m 3]≥ E [X 1 2] E [X 2 2 m 2] E [X 3 …

A combinatorial proof of the Gaussian product inequality (GPI) is given under the
assumption that each component of a centered Gaussian random vector X=(X 1,…, X d) of …

We prove the three-dimensional Gaussian product inequality (GPI) E [X 1 2 X 2 2 m 2 X 3 2
m 3]≥ E [X 1 2] E [X 2 2 m 2] E [X 3 2 m 3] for any centered Gaussian random vector (X 1, X …

The long-standing Gaussian product inequality (GPI) conjecture states that E [∏ j= 1 n∣ X
j∣ yj]≥∏ j= 1 n E [∣ X j∣ yj] for any centered Gaussian random vector (X 1,…, X n) and …

A Gaussian Inequality for Expected Absolute Products Page 1 J Theor Probab (2012) 25:92–99
DOI 10.1007/s10959-010-0329-0 A Gaussian Inequality for Expected Absolute Products …

We prove a strong form of the Gaussian product conjecture in dimension three. Our purely
analytical proof simplifies previously known proofs based on combinatorial methods or …