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Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is in a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch? see an image here

Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is in a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch?

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Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is in a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch? see an image here

Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is in a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch? see an image here

Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch?

Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is in a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch? see an image here