Topic

# Limit (mathematics)

About: Limit (mathematics) is a research topic. Over the lifetime, 27204 publications have been published within this topic receiving 405890 citations.

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3,423 citations

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TL;DR: In this paper, it was shown that the super-conformal field theory on the brane decouples from the bulk of the field theory in a low energy limit.

Abstract: We show that the large $N$ limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large $N$. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 4-d ${\cal N} =4$ super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.

3,136 citations

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TL;DR: In this paper, the bias of LSDV for dynamic panel data models can be sizeable, even when T = 20, and a corrected LSDV estimator is the best choice overall.

Abstract: Using a Monte Carlo approach, we find that the bias of LSDV for dynamic panel data models can be sizeable, even when T =20. A corrected LSDV estimator is the best choice overall, but practical considerations may limit its applicability. GMM is a second best solution and, for long panels, the computationally simpler Anderson–Hsiao estimator performs well.

2,168 citations

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TL;DR: The authors showed that the coefficients obtained from using Tobit-here called "beta" coefficients -provide more information than is commonly realized and showed that this decomposition can be quantified in rather useful and insightful ways.

Abstract: In this paper authors point out that the coefficients obtained from using Tobit-here called "beta" coefficients - provide more information than is commonly realized. In particular, authors show that Tobit can be used to determine both changes in the probability of being above the limit and changes in the value of the dependent variable if it is already above the limit$ and authors show that this decomposition can be quantified in rather useful and insightful ways.

1,960 citations

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TL;DR: In this paper, the authors show how the concentration-compactness principle has to be modified in order to be able to treat this class of problems and present applications to Functional Analysis, Mathematical Physics, Differential Geometry and Harmonic Analysis.

Abstract: After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in RN where the invariance of RN by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness principle has to be modified in order to be able to treat this class of problems and we present applications to Functional Analysis, Mathematical Physics, Differential Geometry and Harmonic Analysis.

1,931 citations