# Random Matrices with Multiple Distributions

I am investigating a problem in engineering and using a matrix model for it. I am wondering if someone can point some keywords or existing literature the treats such a problem.

I basically assume to have a random KxN matrix G which is constructed as follows. For every column $1 \leq i \leq N$ a number $1 \leq d \leq K$ is randomly sampled from distribution $\rho_1(i)$. Then d elements of column i are selected according to probability distribution $\rho_2(d)$.

Is there a mathematical model that treats such problem and gives results on the resulting matrix?

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