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20 papers · 1 filter
Optimal Weighted Poincaré and Log-Sobolev Inequalities for Cauchy Measures
Zhengliang Zhang, Bin Qian, Wei Liu
In this paper, We establish the weighted Poincaré inequalities and Log-Sobolev inequalities for Cauchy distributions with optimal weight functions.
On barycentric subdivision, with simulations
Persi Diaconis, Laurent Miclo
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives r…
Weighted Poincaré-type inequalities for Cauchy and other convex measures
Sergey G. Bobkov, Michel Ledoux
Brascamp--Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general -concave probability measure…
A note on Talagrand's transportation inequality and logarithmic Sobolev inequality
Patrick Cattiaux, Arnaud Guillin, Liming Wu
We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality.…
Unifying Practical Uncertainty Representations: II. Clouds
Sebastien Destercke, Didier Dubois, Eric Chojnacki
There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distribu…
Unifying Practical Uncertainty Representations: I. Generalized P-Boxes
Sebastien Destercke, Didier Dubois, Eric Chojnacki
There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability inter…