Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this article, different asymptotic representations for correlation functions of critical integrable systems were discussed, and it was shown that in the one-dimensional boson model, the correlation functions obtained by the multiple-integral method coincides with the conformal field theory predictions in the low-temperature limit.
Abstract: We discuss different asymptotic representations for correlation functions of critical integrable systems. We prove that in the one-dimensional boson model, the asymptotic series for correlation functions obtained by the multiple-integral method coincides with the conformal field theory predictions in the low-temperature limit.
4 citations
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01 Jan 2011TL;DR: In this article, the authors pointed out that an estimator, though asymptotically much less efficient than another, may still have much greater probability concentration than the latter.
Abstract: Partly of an expository nature this note brings out the fact that an estimator, though asymptotically much less efficient (in the classical sense) than another, may yet have much greater probability concentration (as defined in this article) than the latter.
4 citations
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TL;DR: For Fisher's diffusion model which describes the advance of an advantageous gene, the following two questions are discussed: Existence of travelling fronts and convergence to travelling fronts as mentioned in this paper. And there are striking differences between the heterozygote intermediate and the heter-ozygote inferior case.
Abstract: For Fisher’s diffusion model which describes the advance of an advantageous gene, the following two questions are discussed: Existence of travelling fronts and convergence to travelling fronts. There are striking differences between the heterozygote intermediate and the heterozygote inferior case.
4 citations
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4 citations
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01 Jan 1992
TL;DR: This thesis focuses on the single link method and a detailed general framework is developed to deal with hierarchical structure in either the sample or the population case, establishing the equivalence of hierarchies and ultrametric distances, define single-link distances and derive the connection to minimal spanning trees.
Abstract: The main theme of this thesis is the study of the asymptotic and computational aspects of clustering analysis for samples of iid observations in an effort to improve upon the older methods. We are concerned with hierarchical clustering methods and we focus on the single link method. First, a detailed general framework is developed to deal with hierarchical structure in either the sample or the population case. In this general setting, we establish the equivalence of hierarchies and ultrametric distances, define single-link distances and derive the connection to minimal spanning trees. The next step is to study the behavior of single-link distances between iid observations drawn from probability distributions whose support is compact and has a finite number of connected components. For such distributions, we prove the consistency of single-link distances and in the case of one dimensional distributions we obtain an asymptotically normal distribution for the average single link distance using facts about spacings. In the case of multivariate distributions and under some conditions, we obtain the rate of convergence for the maximum single-link distance (which is equal to the length of the longest edge of the minimal spanning tree) and give upper and lower bounds. To deal with the chaining problem in real data, we combine kernel density estimation with the computation of minimal spanning trees to study the effect of density truncation on single-link partitions. New statistics are proposed to help decide on the best truncation level, leading to an improved version of the single-link method. Simulation studies show how these statistics perform with un:modal and bimodal densities. Finally, these tools are applied to two cluster,... xam-ples: One involves grouping several foods according to the nutrients they contain. The other is a market segmentation study, concerning an Atlanta manufacturer of prefabricated homes. ToUr' aCirb roizvvy v iC 6 7rp66Owv A6yo dKrairL , ro !ar 'iv / v a i iroAAcd acbrcv I?/Kdrpov, Ktai mrD1 l • k • 'tpa ci0), dAA& rT& irore dpLO/6v kdrepov lp7rpooOcv CitrirmaL Trof) 6irELp ai'rwv 'EKarac 770ovLivaL; This is exactly what the previous discussion requires from us: How is it possible for each of them to be one and many at the same time and how is it they do not immediately become Infinity but instead they first acquire a finite number before each of them becomes Infinity? Plato, Philebus 19A. To my family, for their love and support. Acknowledgements New ideas …
4 citations