Rosso Santachiara Krauth 2005
From Werner KRAUTH
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| [http://arxiv.org/abs/cond-mat/0503134 Electronic version (from arXiv)] | [http://arxiv.org/abs/cond-mat/0503134 Electronic version (from arXiv)] | ||
| - | [http://iopscience.iop.org/1742-5468/2005/08/L08001 Original paper (may yrequire subscription)] | + | |
| + | [http://iopscience.iop.org/1742-5468/2005/08/L08001/pdf/1742-5468_2005_08_L08001.pdf Original paper (no subscription needed)] | ||
| =Illustration= | =Illustration= | ||
Current revision
A. Rosso, R. Santachiara, W. Krauth Geometry of Gaussian signals Journal of Statistical Mechanics: Theory and Experiment L08001 (2005)
Contents |
Paper
Abstract: We consider Gaussian signals, i.e. random functions $u(t)$ ($t/L \in [0,1]$) with independent Gaussian Fourier modes of variance $\sim 1/q^{\alpha}$, and compute their statistical properties in small windows $[x, x+\delta]$. We determine moments of the probability distribution of the mean square width of $u(t)$ in powers of the window size $\delta$. We show that the moments, in the small-window limit $\delta \ll 1$, become universal, whereas they strongly depend on the boundary conditions of $u(t)$ for larger $\delta$. For $\alpha > 3$, the probability distribution is computed in the small-window limit and shown to be independent of $\alpha$.
Further information:
Electronic version (from arXiv)
Original paper (no subscription needed)
