arXiv subjects

Therese Basa Landry

Publications and source records attributed to Therese Basa Landry.

3 recordsLinked to original sources

arXiv2026

Compact quantum metric spaces from free probability

We study quantum metric space structures on operator algebras arising from free probability, namely those associated to $q$-Gaussians and free Gibbs laws for convex potentials. We note that even for free semicirculars, Voiculescu's dual system does not produce a quantum metric space structure that recovers the weak-$*$ topology on the state space. However, for $q$-Gaussians, we can define a compact quantum metric space using length-like functions by the same method as has already been used for hyperbolic groups, quantum groups of rapid decay, free products, and free graph algebras. Next, motivated by the free transport results for free Gibbs laws, we describe a universal way of defining Lip-norms in terms of a generating set, which behaves well under changes of coordinates. We show using semigroup regularization that this Lip-norm defines a quantum metric space structure for $q$-Gaussians, and then transfer this property to free Gibbs laws for convex potentials using free transport.

math.OA↗

arXiv2025

Quantum Wasserstein distances for quantum permutation groups

We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra.

math.OA↗

arXiv2022

Spectral Triples for Noncommutative Solenoids and a Wiener's lemma

In this paper we construct odd finitely summable spectral triples based on length functions of bounded doubling on noncommutative solenoids. Our spectral triples induce a Leibniz Lip-norm on the state spaces of the noncommutative solenoids, giving them the structure of Leibniz quantum compact metric spaces. By applying methods of R. Floricel and A. Ghorbanpour, we also show that our odd spectral triples on noncommutative solenoids can be considered as direct limits of spectral triples on rotation algebras. In the final section we prove a noncommutative Wiener's lemma and show that our odd spectral triples can be defined to have an associated smooth dense subalgebra which is stable under the holomorphic functional calculus, thus answering a question of B. Long and W. Wu. The construction of the smooth subalgebra also extends to the case of nilpotent discrete groups.

math.OA↗