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- W2325871509 abstract "A particle that is located at the position (0, 0) in the ( x, y ) plane at the moment x = 0 is subjected to random impulses at the moments of time x = 1, 2, …, a + b . As the result of each impulse, the particle may be displaced either by a positive or by a negative step with respect to the y -axis; it is given that the particle is restricted by the condition that it has exactly a positive and b negative displacements. Hence in the ( x, y ) plane the path of the particle at each impulse is depicted by a shift of a unit to the right and by one unit upward or downward; that is the particle's path starts at (0, 0) and terminates at ( a + b, a – b ) after a + b steps. We assume that all possible different paths are equally probable, and assume also, without loss of generality, that a ≧ b." @default.
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- W2325871509 date "1965-12-01" @default.
- W2325871509 modified "2023-10-17" @default.
- W2325871509 title "On some problems concerning a restricted random walk" @default.
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- W2325871509 doi "https://doi.org/10.2307/3212201" @default.
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