From Werner KRAUTH

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-	A. Rosso, R. Santachiara, W. Krauth Geometry of Gaussian signals Journal of Statistical Mechanics: Theory and Experiment L08001 (2005)	+	__FORCETOC__
		+	A. Rosso, R. Santachiara, W. Krauth ''Geometry of Gaussian signals'' Journal of Statistical Mechanics: Theory and Experiment L08001 (2005)
		+
		+	=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:'''
		+
		+	[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)]
		+
		+	=Illustration=
		+
		+
		+	[[Category:Publication]] [[Category:2005]]

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Revision as of 14:01, 27 October 2012

A. Rosso, R. Santachiara, W. Krauth Geometry of Gaussian signals Journal of Statistical Mechanics: Theory and Experiment L08001 (2005)

Contents 1 Paper 2 Illustration

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 (may yrequire subscription)

Illustration