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--- chaosbook:noise [2010/07/01 03:45]
predrag Rice distribution remark
+++ chaosbook:noise [2010/08/04 15:51] (current)
predrag Goldobin and Zaks noisy preprint
@@ Line 14: / Line 14: @@
 <span style="color:green;font-size:80%;text-align:right;">enter the latest posts at the top of this section</span>
 </html>
+**2010-08-03 PC to Domenico** [[http://arxiv.org/abs/1008.0073|Noise reduces disorder in chaotic dynamics]] by Denis S. Goldobin and Michael A. Zaks. They say: "We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and discover a novel noise-induced ordering phenomenon. For long unstable periodic orbits the weights (or natural measure) appear to be highly inhomogeneous over the set either diminishing or enhancing their contribution into system dynamics. We show analytically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing effect, make a regularizing influence on the chaotic dynamics. We demonstrate this universal effect rooted into the nature of deterministic chaos for the Lorenz system. The effect can be observed as shrinking of the distribution of averages over finite segments of the chaotic trajectory and lead to significant enhancement of the coherence of chaotic oscillations."
+**2010-07-02 PC to Sara**
+They probably exist - Google returns lots of hits of type "Rayleigh–Rice distribution"..."Lagruerre polynomials" etc. Check it out. There exist also orthogonal Rice polynomials (hypergeometric functions) but I think they are not related to the Rice distribution.
+**2010-07-01 Sara** What would be really useful is a family of orthogonal PDFs. If you coma across such thing ...
 **2010-07-01 PC to Sara**
 Rice distribution (see [[http://en.wikipedia.org/wiki/Rice_distribution|wikipedia]] and MathWorld [[|]]
-might be the right distribution to use in your work on linear-nonlinear models. I was told that it describes the distribution of distances between two random events. There is also a [[http://mathworld.wolfram.com/RayleighDistribution.html|Rayleigh Distribution]].
+might be the right distribution to use in your work on linear-nonlinear models. I was told that it describes the distribution of distances between two random events. There is also a [[http://mathworld.wolfram.com/RayleighDistribution.html|Rayleigh Distribution]]. The original paper is [[http://www.cramster.com/reference/wiki.aspx?wiki_name=Stephen_O._Rice|Stephen O. Rice]], "Statistical properties of a sine wave plus
+random noise," //Bell Syst. Tech. J//. **22** 109–57 (1948 ).
+[7] Nakagami M 1960 The m-distribution—a general formula
 **2010-04-07 PC** In Goettingen Mirko ... and David Hofmann have started an interesting [[http://www.nld.ds.mpg.de/~langevin/|Stochastic Processes Seminar]].

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