Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities
We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin–Stein method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires minimal moment ass...
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics
2025
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| _version_ | 1824459273184215040 |
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| author | Trauthwein, T |
| author_facet | Trauthwein, T |
| author_sort | Trauthwein, T |
| collection | OXFORD |
| description | We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals.
Combining these with the Malliavin–Stein method, we derive bounds in the
Wasserstein and Kolmogorov distances whose application requires minimal
moment assumptions on add-one cost operators — thereby extending the results from (Last, Peccati and Schulte, 2016). Our applications include a central limit theorem (CLT) for the Online Nearest Neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also
apply our techniques to derive quantitative CLTs for edge functionals of the
Gilbert graph, of the k-Nearest Neighbour graph and of the Radial Spanning
Tree. In most cases, even the qualitative CLTs are new. |
| first_indexed | 2025-02-19T04:39:10Z |
| format | Journal article |
| id | oxford-uuid:307878c5-8ed5-499b-92ff-dbf9f908fdb8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:39:10Z |
| publishDate | 2025 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:307878c5-8ed5-499b-92ff-dbf9f908fdb82025-02-14T16:40:39ZQuantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalitiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:307878c5-8ed5-499b-92ff-dbf9f908fdb8EnglishSymplectic ElementsInstitute of Mathematical Statistics2025Trauthwein, TWe establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin–Stein method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires minimal moment assumptions on add-one cost operators — thereby extending the results from (Last, Peccati and Schulte, 2016). Our applications include a central limit theorem (CLT) for the Online Nearest Neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the k-Nearest Neighbour graph and of the Radial Spanning Tree. In most cases, even the qualitative CLTs are new. |
| spellingShingle | Trauthwein, T Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title | Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title_full | Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title_fullStr | Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title_full_unstemmed | Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title_short | Quantitative CLTs on the Poisson space via Skorohod estimates and p-Poincaré inequalities |
| title_sort | quantitative clts on the poisson space via skorohod estimates and p poincare inequalities |
| work_keys_str_mv | AT trauthweint quantitativecltsonthepoissonspaceviaskorohodestimatesandppoincareinequalities |