Densities of Short Uniform Random Walks
نویسندگان
چکیده
منابع مشابه
Densities of short uniform random walks
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. We also present some new results concerning the moments of uniform random walks, in particular their derivatives.
متن کاملDensities of short uniform random walks in higher dimensions
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the twodimensional case.
متن کاملDensities of Short Uniform Random Walks with an appendix
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect si...
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Given εi ∈ [0,1) for each 1 < i < n, a particle performs the following random walk on {1,2, . . . ,n}: If the particle is at n, it chooses a point uniformly at random (u.a.r.) from {1, . . . ,n− 1}. If the current position of the particle is m (1 < m < n), with probability εm it decides to go back, in which case it chooses a point u.a.r. from {m + 1, . . . ,n}. With probability 1− εm it decides...
متن کاملShort Hyperuniform Random Walks
Random walks of two steps, with fixed sums of lengths of 1, taken into uniformly random directions in d-dimensional Euclidean spaces (d ≥ 2) are investigated to construct continuous step-length distributions which make them hyperuniform. The endpoint positions of hyperuniform walks are spread out in the unit ball as the projections in the walk space of points uniformly distributed on the surfac...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2012
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-079-2