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This problem is some variation of another MO question. Consider the matrix $$M_n:=\begin{bmatrix}-c& a & a& \dots & a \\ b & c & a& \ddots & a\\ b & b & -c &...

Does anyone know anything about the determinant of a random $n\times n$ row stochastic matrix? What I have in mind is that the rows are independently selected from the uniform distribution on the unit ...

This is a variant of another MO question. Consider the matrix $$M_n:=\begin{bmatrix}c_1& a & b&a& \ddots & a \\ b & c_2 & a& b&\ddots & b\\ a & b & c_3&...

Let $p_1, p_2,\dots, p_n$ and $q_1,q_2,\dots,q_n$ be a collection of complex polynomials. Let $A$ be a $n \times n$ matrix satisfying $$a_{ij} = \begin{cases} p_i(x) & \text{ if } i = j, \\ q_i(x)...