Khusanbaev, Ya. M. On a theorem of Poisson for combinatorial sums. (Russian) Zbl 0697.60036 Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk 1989, No. 5, 43-47 (1989). Let \(X_ n=\{X(i,j)\), \(1\leq i,j\leq n\}\) be a matrix with random elements taking the values 0 or 1 such that the rows of \(X_ n\) are independent random vectors. Let \(R=(R_ 1,...,R_ n)\) be a random vector uniformly distributed on the set of all permutations of positive integers 1,...,n. Sufficient conditions are given for the convergence in Skorokhod’s J- topology of the process \[ S_ n(t)=\sum^{[nt]}_{i=1}X(i,R_ i),\quad 0\leq t\leq 1, \] to the Poisson one. The closeness of the distributions of \(S_ n(1)\) to the Poisson one is estimated. Reviewer: T.Shervashidze MSC: 60F17 Functional limit theorems; invariance principles 60F05 Central limit and other weak theorems Keywords:Poisson processes; matrix with random elements; convergence in Skorokhod’s J-topology PDFBibTeX XMLCite \textit{Ya. M. Khusanbaev}, Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk 1989, No. 5, 43--47 (1989; Zbl 0697.60036)