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Wasserstein geometry and Ricci curvature bounds for Poisson spaces (2024)
Journal Article
Dello Schiavo, L., Herry, R., & Suzuki, K. (2024). Wasserstein geometry and Ricci curvature bounds for Poisson spaces. Journal de l’École polytechnique — Mathématiques, 11, 957-1010. https://doi.org/10.5802/jep.270

We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Bre... Read More about Wasserstein geometry and Ricci curvature bounds for Poisson spaces.

On the ergodicity of interacting particle systems under number rigidity (2023)
Journal Article
Suzuki, K. (2024). On the ergodicity of interacting particle systems under number rigidity. Probability Theory and Related Fields, 188(1-2), 583-623. https://doi.org/10.1007/s00440-023-01243-3

In this paper, we provide relations among the following properties: the tail triviality of a probability measure μ on the configuration space Υ; the finiteness of a suitable L2-transportation-type distance d¯Υ; the irreducibility of local μ-symmetric... Read More about On the ergodicity of interacting particle systems under number rigidity.

Removable sets and Lp-uniqueness on manifolds and metric measure spaces (2023)
Journal Article
Hinz, M., Masamune, J., & Suzuki, K. (2023). Removable sets and Lp-uniqueness on manifolds and metric measure spaces. Nonlinear Analysis: Theory, Methods and Applications, 234, https://doi.org/10.1016/j.na.2023.113296

We study symmetric diffusion operators on metric measure spaces. Our main question is whether essential self-adjointness or -uniqueness are preserved under the removal of a small closed set from the space. We provide characterizations of the critical... Read More about Removable sets and Lp-uniqueness on manifolds and metric measure spaces.

Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds (2022)
Journal Article
Suzuki, K. (2022). Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXIII(2), 745-808. https://doi.org/10.2422/2036-2145.201911_001

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the stability... Read More about Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds.

Sobolev-to-Lipschitz property on $${\mathsf {QCD}}$$-spaces and applications (2021)
Journal Article
Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on $${\mathsf {QCD}}$$-spaces and applications. Mathematische Annalen, 384, 1815-1832. https://doi.org/10.1007/s00208-021-02331-2

We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the correspondi... Read More about Sobolev-to-Lipschitz property on $${\mathsf {QCD}}$$-spaces and applications.

Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces (2021)
Journal Article
Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis, 281(11), Article 109234. https://doi.org/10.1016/j.jfa.2021.109234

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As... Read More about Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces.

Convergence of Brownian motions on metric measure spaces under Riemannian Curvature–Dimension conditions (2019)
Journal Article
Suzuki, K. (2019). Convergence of Brownian motions on metric measure spaces under Riemannian Curvature–Dimension conditions. Electronic Journal of Probability, 24, Article 102. https://doi.org/10.1214/19-ejp346

We show that the pointed measured Gromov convergence of the underlying spaces implies (or under some condition, is equivalent to) the weak convergence of Brownian motions under Riemannian Curvature-Dimension conditions.

Convergence of non-symmetric diffusion processes on RCD spaces (2018)
Journal Article
Suzuki, K. (2018). Convergence of non-symmetric diffusion processes on RCD spaces. Calculus of Variations and Partial Differential Equations, 57(5), Article 120. https://doi.org/10.1007/s00526-018-1398-7

We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli (Mem Am M... Read More about Convergence of non-symmetric diffusion processes on RCD spaces.