Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: The theory of the variation of the depth of amplitude scintillations with the zenith angle of the source is considered in this article, for radio waves received from a star or a satellite.
367 citations
TL;DR: In this article, the authors discuss the persistence and related first-passage properties in extended many-body nonequilibrium systems and discuss various generalizations of the local site persistence probability.
Abstract: In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spin models undergoing phase-ordering dynamics, diffusion equation, fluctuating interfaces, etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalizations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon var...
357 citations
TL;DR: In this article, a survey on sample function properties of Gaussian processes with the main emphasis on boundedness and continuity, including Holder conditions locally and globally, is presented, along with a discussion of sample functions.
Abstract: This is a survey on sample function properties of Gaussian processes with the main emphasis on boundedness and continuity, including Holder conditions locally and globally. Many other sample function properties are briefly treated.
350 citations
TL;DR: In this paper, a theoretical expression for the joint distribution of wave period and amplitude, which was previously derived for a Gaussian record with a narrow spectrum, is restated in simple form.
Abstract: A theoretical expression for the joint distribution of wave period and amplitude, which was previously derived for a Gaussian record with a narrow spectrum, is restated in simple form. According to this distribution the variability of wave periods, for waves of a given height, is inversely proportional to the wave height, so that the higher waves tend to be more regular. The distribution is found to agree well with some observations of wave periods and amplitudes from the Gulf of Mexico, as given by Bretschneider (1959).
320 citations
01 Dec 1958
TL;DR: In this article, the distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν0 is analyzed by associating the photons with Gaussian random waves, leading to a full statistical description of the counts.
Abstract: The distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν0 is analysed by associating the photons with Gaussian random waves. This is shown to lead to a full statistical description of the counts. It is shown that the number nT in a time interval T > 1/Δν0 are simply the density fluctuations of a boson assembly in a phase space of ~ Δν0T cells. The correlation coefficient ρ of the fluctuations of counts from two detectors illuminated by partially coherent beams is found to be proportional to the local time average of the square of the coherence function γ122. The correlation is shown to depend on the degeneracy of the beams in such a way that ρ → 2γ122 for highly degenerate beams. The results are all consistent with those obtained by Hanbury Brown and Twiss in 1957.
316 citations