15 citations · 57 across the 22 of their papers we have counts for
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A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy
Melchior Wirth
We study quantum Dirichlet forms and the associated symmetric quantum Markov semigroups on noncommutative spaces. It is known from the work of Cipriani and Sauvageot that the…
On the geometry of geodesics in discrete optimal transport
Matthias Erbar, Jan Maas, Melchior Wirth
We consider the space of probability measures on a discrete set , endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset $Y \sub…
Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure
Bobo Hua, Matthias Keller, Michael Schwarz +1
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities an…
Geometric properties of Dirichlet forms under order isomorphisms
Daniel Lenz, Marcel Schmidt, Melchior Wirth
We study pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated -spaces. We consider the measurable, the topological and the geometric s…