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On an algorithm for calculating the potential of a simple random walk on a cubic lattice. (Russian) Zbl 0738.65105
The authors construct an algorithm for the computation of the potential of a simple random walk on a three-dimensional cubic lattice. The potential is defined as \[ G(l,m,n)={3\over 8\pi^ 3}\int^{2\pi}_ 0\int^{2\pi}_ 0\int^{2\pi}_ 0{\cos(l\varphi+m\psi+n\theta)d \varphi d\psi d\theta\over 3-\cos \varphi-\cos \psi-\cos \theta}. \] The evaluation of \(k\) decimal points of \(G\) by means of the proposed algorithm is of the same complexity as the multiplication of \(k\)-digit numbers.

65C99 Probabilistic methods, stochastic differential equations
65D32 Numerical quadrature and cubature formulas
65Y20 Complexity and performance of numerical algorithms
60G50 Sums of independent random variables; random walks