Eikonal Blog

2010.06.30

Jaggedness

Filed under: mathematics — Tags: — sandokan65 @ 22:17

The Jaggedness of a discrete path c_N=\{x_i \in {\Bbb R}|i=0,N| x_0=a, x_N=b\} is defined by:

J = \frac1{N-1} \sum_{i=0}^{N-2} \frac12 (1-\hbox{sign}(\Delta x_i \Delta x_{i+1}))

where \Delta x_i :\equiv x_{i+1} - x_i.

Source: “Jaggedness of Path Integral Trajectories” by Aleksandar Bogojevic, Antun Balaz, Aleksandar Belic (2005.09.10) – http://arxiv.org/abs/cond-mat/0509266.

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