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Distributions of absolute central moments for random walk surfaces

A J McKane·R K P Zia
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Abstract

We study periodic Brownian paths, wrapped around the surface of a cylinder. One characteristic of such a path is its width square, $w^2$, defined as its variance. Though the average of $w^2$ over all possible paths is well known, its full distribution function was investigated only recently. Generalising $w^2$ to $w^{(N)}$, defined as the $N$-th power of the {\it magnitude} of the deviations of the path from its mean, we show that the distribution functions of these also scale and obtain the asymptotic behaviour for both large and small $w^{(N)}$.

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A J McKane, R K P Zia. 1995-09-20. Distributions of absolute central moments for random walk surfaces. https://doi.org/10.1088/0305-4470%2F29%2F6%2F006

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