MathOverflow

Let $X_i$ ($i=1, \dots$) be an orthonormal basis for $L^2(\Omega, \mathbb P)$. In particular, it holds that $$\mathbb E[X_iX_j] = \delta_{ij}.$$Now take $Z\in L^2(\Omega, \mathbb P)$ and define $\tilde X_i:=ZX_i$. Let $\Sigma_m$ be the covariance matrix...

I hope this is a suitable MO question. Lets say I have a series of related functions whose asmyptotic growth is known:
\begin{equation}f_c(A,B) = \Theta((A-B) \log\log(B))\end{equation}\begin{equation}g_c(A,B) = \Theta((A-B) \log\log(B))\end{equation}\begin{equation}h_c(A,B) = \Theta((A-B) \log\log(B))\end{equation}...

I am studying a parameter–dependent quintic polynomial that arises from a dimensionless “master equation” for the photon sphere in a certain black hole model. After nondimensionalization and elimination of auxiliary parameters, the equation reduces to...

In the paper "A Gaussian measure on $l^{\infty}$" by Fremlin and Talagrand https://projecteuclid.org/journals/annals-of-probability/volume-8/issue-6/A-Gaussian-Measure-on-linfty/10.1214/aop/1176994583.full, a Gaussian probability measure $\gamma$ on...