%0 Generic %1 schneider2019concentration %A Schneider, Friedrich Martin %A Solecki, Sławomir %D 2019 %K concentration logic measure %T Concentration of measure, classification of submeasures, and dynamics of $L_0$ %U http://arxiv.org/abs/1907.12686 %X Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to the metric induced by a weighted covering of the index set of the product. Our proof combines the Herbst argument with an entropic version of the weighted Loomis--Whitney inequality. We give a quantitative "geometric" classification of diffused submeasures into elliptic, parabolic, and hyperbolic. We prove that any non-elliptic submeasure (for example, any measure, or any pathological submeasure) has a property that we call covering concentration. Our results have strong consequences for the dynamics of the corresponding topological $L_0$-groups.

@misc{schneider2019concentration, abstract = {Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to the metric induced by a weighted covering of the index set of the product. Our proof combines the Herbst argument with an entropic version of the weighted Loomis--Whitney inequality. We give a quantitative "geometric" classification of diffused submeasures into elliptic, parabolic, and hyperbolic. We prove that any non-elliptic submeasure (for example, any measure, or any pathological submeasure) has a property that we call covering concentration. Our results have strong consequences for the dynamics of the corresponding topological $L_0$-groups.}, added-at = {2019-07-31T13:20:41.000+0200}, author = {Schneider, Friedrich Martin and Solecki, Sławomir}, biburl = {https://www.bibsonomy.org/bibtex/2fcef2f446180cb240b39575145f610a1/tomhanika}, description = {Concentration of measure, classification of submeasures, and dynamics of $L_{0}$}, interhash = {13bd3ba69bc72c10eac40e53dd8973df}, intrahash = {fcef2f446180cb240b39575145f610a1}, keywords = {concentration logic measure}, note = {cite arxiv:1907.12686}, timestamp = {2019-07-31T13:20:41.000+0200}, title = {Concentration of measure, classification of submeasures, and dynamics of $L_{0}$}, url = {http://arxiv.org/abs/1907.12686}, year = 2019 }