We present a Gaussian correlation inequality which is closely related to a result of Schechtman, Schlumprecht and Zinn (1998) on the well-known Gaussian correlation conjecture. The usefulness of the inequality is demonstrated by several important applications to the estimates of small ball probability.
"A Gaussian Correlation Inequality and its Applications to Small Ball Probabilities." Electron. Commun. Probab. 4 111 - 118, 1999. https://doi.org/10.1214/ECP.v4-1012