scholarly journals Monotonicity in the averaging process

2021 ◽  
Author(s):  
Eli Ben-Naim ◽  
Paul L Krapivsky
Keyword(s):  
Continuous Spectrum ◽  
Elementary Step ◽  
Statistical Properties ◽  
Two Agents ◽  
Interacting Agents ◽  
Self Similar

Abstract We investigate an averaging process that describes how interacting agents approach consensus through binary interactions. In each elementary step, two agents are selected at random and they reach compromise by adopting their opinion average. We show that the fraction of agents with a monotonically decreasing opinion decays as $e^{-\alpha t}$, and that the exponent $\alpha=\tfrac{1}{2}-\tfrac{1+\ln \ln 2}{4\ln 2}$ is selected as the extremum from a continuous spectrum of possible values. The opinion distribution of monotonic agents is asymmetric, and it becomes self-similar at large times. Furthermore, the tails of the opinion distribution are algebraic, and they are characterized by two distinct and nontrivial exponents. We also explore statistical properties of agents with an opinion strictly above average.

scholarly journals Singularly continuous spectrum of a self-similar Laplacian on the half-line

2016 ◽  
Vol 57 (5) ◽  
pp. 052104 ◽  
Author(s):  
Joe P. Chen ◽  
Alexander Teplyaev
Keyword(s):  
Continuous Spectrum ◽  
Half Line ◽  
Self Similar

Measurements of concentration fluctuations in relative turbulent diffusion

1979 ◽  
Vol 94 (1) ◽  
pp. 83-101 ◽  
Author(s):  
P. C. Chatwin ◽  
Paul J. Sullivan
Keyword(s):  
Spatial Resolution ◽  
Molecular Diffusion ◽  
Statistical Properties ◽  
Concentration Fluctuations ◽  
Recent Analysis ◽  
Critical Examination ◽  
Natural Environments ◽  
Central Regions ◽  
Self Similar ◽  
The Mean

In 1965 Sullivan made many measurements of concentration in dye plumes in the surface layer of Lake Huron with the primary purpose of estimating the distance–neighbour function (Sullivan 1965, 1971). This paper presents the results of a recent analysis of the concentration fluctuations in these experiments for, despite their great practical and theoretical importance, there are very few published reports of such measurements from natural environments. One reason for this apparent neglect has undoubtedly been the anticipated high noise level, and the present results confirm this expectation. The experimental analysis uses the framework of relative diffusion since this has great advantages compared with that of absolute diffusion. Despite the noise, the results are consistent, to the degree of spatial resolution attained, with the self-similar structure anticipated for relative, but not absolute, diffusion. Further interesting features of the results are that changes in the form of the statistical properties across the plume indicate an unexpectedly strong influence of the central regions, and that certain statistical properties have much less noisy profiles than that of the mean square fluctuations. The influence of molecular diffusion is shown to be strong. Interpretation of the results is based partly on the extension of the theory recently developed by Chatwin & Sullivan (1979a) for a cloud, although the limited spatial resolution attained did not allow direct critical examination of this work.

scholarly journals Statistical properties of galaxy distributions

1996 ◽  
Vol 3 (4) ◽  
pp. 274-283 ◽  
Author(s):  
F. Sylos Labini ◽  
L. Pietronero
Keyword(s):  
Statistical Physics ◽  
Three Dimensional ◽  
Theoretical Framework ◽  
Statistical Properties ◽  
Matter Distribution ◽  
Direct Study ◽  
Spatial Properties ◽  
Homogeneity Assumption ◽  
Luminous Matter ◽  
Self Similar

Abstract. The recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods modern statistical Physics. These methods which able to identify self-similar and non-analytical prop ties, allow us to test the usual homogeneity assumption of luminous matter distribution. We conclude that both the three dimensional prop ties, and the angular log N - log S relation, point out the fact that the distribution of galaxies and clusters fractal with D ≈ 2 up to the deepest scale probed luminous matter (≈≥ 1000h-1 Mpc). This result has important implications for the theoretical framework that should be adopted.

scholarly journals SELF-SIMILARITY IN THE TAXONOMIC CLASSIFICATION OF HUMAN LANGUAGES

2001 ◽  
Vol 04 (02n03) ◽  
pp. 281-286 ◽  
Author(s):  
DAMIAN H. ZANETTE
Keyword(s):  
Long Range ◽  
Power Law ◽  
Biological Species ◽  
Statistical Properties ◽  
Taxonomic Classification ◽  
Self Similarity ◽  
Self Similar ◽  
Evolutionary Foundation ◽  
Language Classification

Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to each member decays as a power law. This feature reveals that a self-similar structure underlies the taxonomy of languages, exactly as observed in the taxonomic classification of biological species. Such an analogy is a clue to the evolutionary foundation of language classification based on long-range comparison.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar

Statistical properties of type I intermittency

1982 ◽  
Vol 43 (4) ◽  
pp. 585-589 ◽  
Author(s):  
M. N. Bussac ◽  
C. Meunier
Keyword(s):  
Statistical Properties ◽  
Type I
Sign in / Sign up

Export Citation Format

Share Document