Limit distribution of the probabilities of the permanent of a random matrix in the field $\operatorname{GF}(p)$
Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 3-13
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We prove that the permanent $\per(A_{nm})$ of a random $n\times m$ matrix
$A_{nm}$ with elements from $\GF(p)$ and independent rows
has the limit distribution of the form
\[
p_k = \lim_{n\to\infty} \P\{\per(A_{nm}) = k\}
= \rho_m\delta_{k0} + (1-\rho_m)/p, \qquad k=0,1,2,\ldots,p-1,
\]
where $\delta_{k0}$ is Kronecker's symbol. This distribution for each $m$
coincides with the probability distribution of some function of independent
random variables uniformly distributed on $\GF(p)$.This work was supported by the Russian Foundation of Basic Research, Grant 93–011–1443.
@article{DM_1996_8_2_a0,
author = {L. A. Lyapkov and B. A. Sevast'yanov},
title = {Limit distribution of the probabilities of the permanent of a random matrix in the field $\operatorname{GF}(p)$},
journal = {Diskretnaya Matematika},
pages = {3--13},
publisher = {mathdoc},
volume = {8},
number = {2},
year = {1996},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1996_8_2_a0/}
}
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AU - B. A. Sevast'yanov
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PY - 1996
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L. A. Lyapkov; B. A. Sevast'yanov. Limit distribution of the probabilities of the permanent of a random matrix in the field $\operatorname{GF}(p)$. Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/DM_1996_8_2_a0/