Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability that product of real random matrices have all eigenvalues
  real tend to 1   In this article we consider products of real random matrices with fixed size.
Let $A_1,A_2, \dots $ be i.i.d $k \times k$ real matrices, whose entries are
independent and identically distributed from probability measure $\mu$. Let
$X_n = A_1A_2\dots A_n$. Then it is conjectured that $$\mathbb{P}(X_n \text{
has all real eigenvalues}) \rightarrow 1 \text{ as } n \rightarrow \infty.$$ We
show that the conjecture is true when $\mu$ has an atom.

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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an