Geodesic
On the distribution of the number of solutions of random systems of equations which are known to be consistent
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 430-437

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The distribution of the number of solutions of the systems in which each equation is specified by the substitution into a function $\varphi(u_1,\dots,u_d)$, $u_j\in\{0,1\}$, binary unknowns taken at random and without replacement from the set $\{x_1,\dots,x_n\}$, $n\ge d$, is studied. It is proved that, under certain conditions the distribution of the logarithm to base 2 of the number of solutions of the obtained system converges to a Poisson distribution.
Keywords: random systems of equations, the number of solutions
Mots-clés : true solution, Poisson distribution. 
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     author = {V. A. Kopyttsev},
     title = {On the distribution of the number of solutions of random systems of equations which are known to be consistent},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {430--437},
     publisher = {mathdoc},
     volume = {40},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a15/}
}
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V. A. Kopyttsev. On the distribution of the number of solutions of random systems of equations which are known to be consistent. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 430-437. http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a15/