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35 years of the Inverse Tangent Law

机译:反正切定律的35年

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The distribution functions of the solutions of the systems of linear algebraic equations (SLAE) E_n Ex_n D E y_n, in general, have a cumbersome form; the order of these systems in some practical problems is large, therefore, the asymptotic behavior of the solutions should be studied in increasing order n of the system to infinity. A general form of the limit theorems of solutions of the systems of linear algebraic equationsE_nx_n=y_n y~T_n={n~(n)_i,i D 1; ...; n} with independent random coefficients E_n/ij and components n~(n)_i , i; j D 1;...; n, are givenin this survey. By the tradition of choosing the names of laws in probability theory (Arcsine law, Law of iterated logarithm, etc.) we call the unusual behavior of the solutions of (SLAERC) as Inverse Tangent Law.
机译:通常,线性代数方程组(SLAE)E_n Ex_n D E y_n的解的分布函数具有繁琐的形式。这些系统在某些实际问题中的阶数很大,因此,应该以系统的阶数n增至无穷大来研究解的渐近行为。线性代数方程组的解的极限定理的一般形式E_nx_n = y_n y〜T_n = {n〜(n)_i,i D 1; ...; n}具有独立的随机系数E_n / ij和分量n〜(n)_i,i; j D 1; ...; n,在此调查中给出。通过在概率论中选择法律名称的传统(反正弦定律,对数迭代定律等),我们将(SLAERC)解的异常行为称为反正切定律。

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