Calculation of limit probabilities of the distribution of permanent of a random matrix over the field $GF(p)$

We suggest an algorithm calculating the limit probabilities
$$ \lim_{n\to\infty}\mathbf P\{\operatorname{per}(A_{mn})=k\},\qquad k=0,1,2,\dots,p-1,\quad m=1,2,3,\dots, $$
of the distribution of the permanent of a random matrix $A_{mn}=\|\alpha _{ij}\|$ with $m$ rows and $n$ independent columns over the field $GF(p)$.