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We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...
We propose new measures that distinguish and classify entangled states. The measures are
algebraic invariants of linear maps associated with the states. Considering qubits as well as higher spin syst...
Optimal transport for multifractal random measures. Applications
Random measures multifractal processes optimal transport metric KPZ
2010/11/26
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new not...
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
2010/12/14
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...