Central limit theorems for random permanents with correlation structure (Q5960454)

Central limit theorems of random \(m\times n\) matrices of i.i.d. columns with a common intercomponent correlation as \(n-m\to\infty\) are derived. Problems of this kind of permanents of one-dimensional projection matrices and some related themes have been studied by many authors, e.g. \textit{G. J. Szekely} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 59, 355-359 (1982; Zbl 0468.60029)], \textit{A. J. van Es} and \textit{R. Helmers} [Probab. Theory Relat. Fields 80, No. 1, 21-35 (1988; Zbl 0638.60028)], \textit{Yu. V. Borovskikh} and \textit{V. S. Korolyuk} [Acta Appl. Math. 36, No. 3, 227-288 (1994; Zbl 0813.60025), in: Probability theory and mathematical statistics, 176-187 (1992) and Ukr. Math. J. 47, No. 7, 1058-1064 (1995); translation from Ukr. Mat. Zh. 47, No. 7, 922-927 (1995; Zbl 0941.60047)], \textit{E. Yu. Kaneva} [ibid. 47, No. 7, 1148-1151 (1995), resp. ibid. 47, No. 7, 1002-1005 (1995; Zbl 0946.60022)], \textit{E. Yu. Kaneva} and \textit{V. S. Korolyuk} [ibid. 48, No. 1, 48-55 (1996), resp. ibid. 48, No. 1, 44-49 (1996; Zbl 0948.60016)] and \textit{G. J. Székely} and \textit{L. Szeidl} [in: Exploring stochastic laws, 443-455 (1995; Zbl 0968.60025)]. The new results are obtained by introducing a Heoffding-like orthogonal decomposition of a random permanent and deriving the variance formulae for a permanent with the homogeneous correlation structure. 13 references are given.