arXiv subjects
Publications and source records attributed to A J McKane.
The formalism which has been developed to give general expressions for the determinants of differential operators is extended to the physically interesting situation where these operators have a zero mode which has been extracted. In the approach adopted here, this mode is removed by a novel regularisation procedure, which allows remarkably simple expressions for these determinants to be derived.
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 $w^{(N)}$.