Recovering a Gaussian distribution from its minimum

Abstract

Let $X=(X_1,X_2,X_3)$ be a Gaussian random vector such that $X\sim \mathcal{N}(0,\Sigma )$. We consider the problem of determining the matrix $\Sigma$, up to permutation, based on the knowledge of the distribution of $X_{\min }:=\min (X_1,X_2,X_3)$. Particularly, we establish a connection between this identification problem and a geometric identification problem in the context of the theory of the circular radon transform.

References in corpus (1)

• On the injectivity of the circular Radon transform arising in thermoacoustic tomography