Sequences of operator algebras converging to odd spheres in the quantum Gromov–Hausdorff distance
Indian Journal of Pure and Applied MathematicsMarc Rieffel had introduced the notion of the quantum Gromov-Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on $2$-sphere in this distance. One finds applications of similar approximations in many places in the theoretical physics literature. In this paper,
Bhattacharyya, T, Singla, S
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Moduli spaces of compact RCD(0,N)-structures. [PDF]
Math Ann, 2023 Mondino A, Navarro D.
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On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. [PDF]
Calc Var Partial Differ Equ, 2022 Antonelli G +3 more
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Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance. [PDF]
Neuroimage, 2023 Chung MK +9 more
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Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces
, 2020 Given metric quotients $S$ and $S_n$, $n \in \mathbb{N}$, of a metric space $X$, sufficient conditions are provided on the data defining them guaranteeing that $S$ is the Gromov-Hausdorff limit of $S_n$. These conditions are recognized within metric quotients of plane polygons determined by side-pairings known as plain paper-folding schemes.
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Lipschitz Carnot-Carathéodory Structures and their Limits. [PDF]
J Dyn Control Syst, 2023 Antonelli G +2 more
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Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
, 2001 On looking at the literature associated with string theory one finds statements that a sequence of matrix algebras converges to the 2-sphere (or to other spaces). There is often careful bookkeeping with lengths, which suggests that one is dealing with ``quantum metric spaces''.
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Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative. [PDF]
Probab Theory Relat Fields, 2022 Aoun R, Sert C.
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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. [PDF]
Front Artif Intell, 2021 Chazal F, Michel B.
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Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to the spacetime reconstruction problem from causal set theory.
Braun, Mathias, Sämann, Clemens
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