Gaussian comparison conjecture for maxima under variance and increment domination
Let X=(X1,…,Xd)\mathbf{X}=(X_1,\ldots,X_d)X=(X1,…,Xd) and Y=(Y1,…,Yd)\mathbf{Y}=(Y_1,\ldots,Y_d)Y=(Y1,…,Yd) be ddd-dimensional Gaussian vectors with common mean μ=(μ1,…,μd)\bm{\mu}=(\mu_1,\ldots,\mu_d)μ=(μ1,…,μd) and covariance matrices…