We study dynamical optimal transport metrics between density matrices associated to
symmetric Dirichlet forms on finite-dimensional C^* C∗-algebras. Our setting covers …

Abstract Discovered by Aldous, Diaconis and Shahshahani in the context of card shuffling,
the cutoff phenomenon has since then been established for a variety of Markov chains …

Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

Discrete time random walks on a finite set naturally translate via a one-to-one
correspondence to discrete Laplace operators. Typically, Ollivier curvature has been …

We extend three related results from the analysis of influences of Boolean functions to the
quantum setting, namely the KKL theorem, Friedgut's Junta theorem and Talagrand's …

Quantum Markov semigroups characterize the time evolution of an important class of open
quantum systems. Studying convergence properties of such a semigroup and determining …

We prove that for a symmetric Markov semigroup, Ricci curvature bounded from below by a
non-positive constant combined with a finite L∞-mixing time implies the modified log …

We characterize Forman curvature lower bounds via contractivity of the Hodge Laplacian
semigroup. We prove that Ollivier and Forman curvature coincide on edges when …

We study quantum Dirichlet forms and the associated symmetric quantum Markov
semigroups on noncommutative $ L^ 2$ spaces. It is known from the work of Cipriani and …

Contractive coupling rates have been recently introduced by Conforti as a tool to establish
convex Sobolev inequalities (including modified log-Sobolev and Poincar\'{e} inequality) for …