Exponential decay of measures and Tauberian theorems

Mimica, Ante

doi:10.1016/j.jmaa.2016.03.042

Cited by 10 publications

(15 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We here cite one Tauberian result that applies to our setup in which we would like to say something about the exponential decay of p given knowledge of the Laplace transformp. The result is Corollary 1.4 from Mimica (2016). It makes use of the concept of a function's "abscissa of convergence" which we define before stating the result.…”

Section: D21 From Laplace Transform To Pareto Tail: a Tauberian Rementioning

confidence: 96%

See 1 more Smart Citation

The Dynamics of Inequality

Gabaix¹,

Lasry²,

Lions³

et al. 2016

Econometrica

317

271

View full text Add to dashboard Cite

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long‐run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high‐growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.

show abstract

Section: D21 From Laplace Transform To Pareto Tail: a Tauberian Rementioning

confidence: 96%

“…The following result is from Mimica (2016). 62 In addition to the "abscissa of convergence" we just defined, it also uses the concept of the "pole" of a function.…”

Section: D21 From Laplace Transform To Pareto Tail: a Tauberian Rementioning

confidence: 99%

The Dynamics of Inequality

Gabaix¹,

Lasry²,

Lions³

et al. 2016

Econometrica

317

271

View full text Add to dashboard Cite

show abstract

“…Therefore M has Pareto tail with the tail index given by s * (again using the Tauberian theorems in Mimica (2016)). We summarize these derivations in the following proposition.…”

Section: Distributions For One-type Economymentioning

confidence: 99%

Firm Growth Through New Establishments

et al. 2019

View full text Add to dashboard Cite

This paper analyzes firm growth along two margins: the extensive margin (adding more establishments) and intensive margin (adding more workers per establishment). We utilize administrative datasets to document the behavior of these two margins in relation to changes in the U.S. firm size distribution. Between 1990 and 2015, we find that the significant increase in average firm size was driven primarily by the expansion along the extensive margin, particularly in superstar firms. We develop a general equilibrium model of endogenous innovation that features both extensive and intensive margins of firm growth. We estimate the model to uncover the fundamental forces that caused the changes over this time period through the lens of our model. We find that, over time, the cost of innovations that lead to new establishments has declined for firms who are innovative in that dimension. Meanwhile, the duration that a firm can enjoy high growth through such innovation became shorter, and firm entry became more costly.

show abstract

“…(10)], all moments of the spectrumŶ 0 ðωÞ are finite, which requires an exponentially fast decay as ω → ∞. (This is a special case of a more general characterisation of exponentially decaying probability measures 51 .) Combining with the large-ω asymptote of the imaginary part, Y 00 ðωÞ ' 1=mω )Ŷ 0 ðωÞ (see "Methods") and using ζðωÞ 1 Y 0 ðωÞ=Ŷ 0 ðωÞ 2 þŶ 00 ðωÞ 2 Â Ã proves that ζðωÞ ' ðmωÞ 2Ŷ0 ðωÞ as ω → ∞ and thus an exponentially fast suppression of the friction.…”

Section: Resultsmentioning

confidence: 99%

Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures

et al. 2020

View full text Add to dashboard Cite

Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.

show abstract

Exponential decay of measures and Tauberian theorems

Cited by 10 publications

References 5 publications

The Dynamics of Inequality

The Dynamics of Inequality

Firm Growth Through New Establishments

Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures

Contact Info

Product

Resources

About