Publications in Scientific Journals:
M. Huesmann:
"Transport cost estimates for random measures in dimension one";
Electronic Communications in Probability,
21
(2016),
paper no. 46;
1
- 10.
English abstract:
http://projecteuclid.org/euclid.ecp/1464709607#abstract
http://projecteuclid.org/euclid.ecp/1464709607
Abstract
We show that there is a sharp threshold in dimension one for the transport cost between the Lebesgue measure λ
and an invariant random measure μ of unit intensity to be finite. We show that for any such random measure the L1 cost is infinite provided that the first central moments E[|n−μ([0,n))|] diverge. Furthermore, we establish simple and sharp criteria, based on the variance of μ([0,n)], for the Lp cost to be finite for 0<p<1.
German abstract:
http://projecteuclid.org/euclid.ecp/1464709607#abstract
http://projecteuclid.org/euclid.ecp/1464709607
Keywords:
optimal transport random measures shift-coupling allocation extra head scheme
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1214/16-ECP4590
Electronic version of the publication:
http://projecteuclid.org/euclid.ecp/1464709607
Created from the Publication Database of the Vienna University of Technology.