Geodesic
Calculation of limit probabilities of the distribution of permanent of a~random matrix over the field~$GF(p)$
Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 3-7.

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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 $GF(p)$. 
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B. A. Sevastyanov. Calculation of limit probabilities of the distribution of permanent of a~random matrix over the field~$GF(p)$. Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 3-7. http://geodesic.mathdoc.fr/item/DM_2010_22_3_a0/

[1] Lyapkov L. A., Sevastyanov B. A., “Raspredelenie veroyatnostei permanenta sluchainoi bulevoi matritsy”, Diskretnaya matematika, 2:2 (1990), 138–144 | MR | Zbl

[2] Lyapkov L. A., Sevastyanov B. A., “Predelnoe raspredelenie veroyatnostei permanenta sluchainoi matritsy v pole $GF(p)$”, Diskretnaya matematika, 8:2 (1996), 3–13 | MR | Zbl