Abstract:
We consider the class of all n×n(0,1)-matrices with
r ones in each row, 2⩽r⩽n.
For a matrix P chosen randomly and equiprobably from this class, we present
sufficient conditions under which the law of large numbers
for the permanent perP is valid in the triangular array scheme
as n→∞ and the parameter
r=r(n)→∞ so that √n=o(r).
A similar problem is solved for random n×n stochastic matrices
whose rows are independent n-dimensional random variables
which are identically distributed by the Dirichlet law
with parameter ν under the condition that
n→∞ and the parameter ν=ν(n)>0 varies so that nν2→∞.
Received: 07.05.1998
Bibliographic databases:
UDC:519.2
Language: Russian
Citation:
A. N. Timashev, “The law of large numbers for permanents of random stochastic matrices”, Diskr. Mat., 11:3 (1999), 91–98; Discrete Math. Appl., 9:4 (1999), 375–383
\Bibitem{Tim99}
\by A.~N.~Timashev
\paper The law of large numbers for permanents of random stochastic matrices
\jour Diskr. Mat.
\yr 1999
\vol 11
\issue 3
\pages 91--98
\mathnet{http://mi.mathnet.ru/dm389}
\crossref{https://doi.org/10.4213/dm389}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1739071}
\zmath{https://zbmath.org/?q=an:0965.15006}
\transl
\jour Discrete Math. Appl.
\yr 1999
\vol 9
\issue 4
\pages 375--383
Linking options:
https://www.mathnet.ru/eng/dm389
https://doi.org/10.4213/dm389
https://www.mathnet.ru/eng/dm/v11/i3/p91
This publication is cited in the following 3 articles:
A. N. Timashev, “The law of large numbers for permanents of random matrices”, Discrete Math. Appl., 15:5 (2005), 513–526
A. A. Levitskaya, “Systems of Random Equations over Finite Algebraic Structures”, Cybern Syst Anal, 41:1 (2005), 67
A. N. Timashev, “On permanents of random doubly stochastic matrices and on asymptotic estimates for the number of Latin rectangles and Latin squares”, Discrete Math. Appl., 12:5 (2002), 431–452