Series expansion for the probability that a random Boolean matrix is of maximal rank
Author:
V. V. Masol
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal:
Theor. Probability and Math. Statist. 70 (2005), 93104
MSC (2000):
Primary 60C05, 15A52, 15A03
Published electronically:
August 5, 2005
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We consider a random matrix in the field and establish relations that allow one to find the coefficients of the expansion of the probability that a given matrix is of maximal rank into a series in powers of a small parameter. We give explicit formulas for the cases of and , .
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V.
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(2001), 102–105 (Ukrainian, with Ukrainian summary); English transl.,
Theory Probab. Math. Statist. 64 (2002), 117–121.
MR
1922957 (2003g:60015)
 2.
V. V. Masol, Explicit representation of some coefficients in the expansion of the random matrix rank distribution in the field , Theory Stoch. Process. 6(22) (2000), no. 34, 122126.
 3.
V. V. Masol, Expansion in terms of powers of small parameter of the maximum rank distribution of a random Boolean matrix, Kibernetika i Sistemnyi Analiz 38 (2002), no. 6, 176180; English transl. in Cybernetics and Systems Analysis 38 (2003), no. 6, 938942.
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Kibernetika (Kiev) 5 (1975), 138–152 (Russian, with
English summary). MR 0458552
(56 #16752)
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A. Levit\cydotskaya, Invariance theorems for a system of random
linear equations over an arbitrary finite ring, Dokl. Akad. Nauk SSSR
263 (1982), no. 2, 289–291 (Russian). MR 650154
(83g:60046)
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C.
Cooper, On the rank of random matrices, Random Structures
Algorithms 16 (2000), no. 2, 209–232. MR 1742352
(2000k:15050), http://dx.doi.org/10.1002/(SICI)10982418(200003)16:2<209::AIDRSA6>3.3.CO;2T
 1.
 V. V. Masol, An expansion in a small parameter of the probability that a random determinant in the field is 1, Teor. Imovirnost. Mat. Stat. 64 (2001), 102105; English transl. in Theor. Probability Math. Statist. 64 (2002), 117121. MR 1922957 (2003g:60015)
 2.
 V. V. Masol, Explicit representation of some coefficients in the expansion of the random matrix rank distribution in the field , Theory Stoch. Process. 6(22) (2000), no. 34, 122126.
 3.
 V. V. Masol, Expansion in terms of powers of small parameter of the maximum rank distribution of a random Boolean matrix, Kibernetika i Sistemnyi Analiz 38 (2002), no. 6, 176180; English transl. in Cybernetics and Systems Analysis 38 (2003), no. 6, 938942.
 4.
 I. N. Kovalenko, Invariance theorems for random Boolean matrices Kibernetika 11 (1975), no. 5, 138152; English transl. in Cybernetics 11 (1976), no. 5, 818834. MR 0458552 (56:16752)
 5.
 A. A. Levitskaya, Invariance theorems for a system of random linear equations over an arbitrary finite ring, Dokl. AN SSSR 263 (1982), no. 2, 289291; English transl. in Soviet Math. Dokl. 25 (1982), 340342. MR 0650154 (83g:60046)
 6.
 C. Cooper, On the rank of random matrices, Random Structures and Algorithms 16 (2000), no. 2, 209232. MR 1742352 (2000k:15050)
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Additional Information
V. V. Masol
Affiliation:
Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
vicamasol@pochtamt.ru
DOI:
http://dx.doi.org/10.1090/S0094900005006332
PII:
S 00949000(05)006332
Received by editor(s):
April 15, 2003
Published electronically:
August 5, 2005
Article copyright:
© Copyright 2005 American Mathematical Society
