Distributions of absolute central moments for random walk surfaces

Details Distributions of absolute central moments for random walk surfaces Distributions of absolute central moments for random walk surfaces

1995-09-20

arxiv.org/abs/cond-mat/9509124v1

Physics

Condensed Matter

Scientific paper

10.1088/0305-4470/29/6/006

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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