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Quantitative stability of barycenters in the Wasserstein space Wasserstein空间中质心的定量稳定性
1区 数学
Probability Theory and Related Fields Pub Date : 2023-10-25 DOI: 10.1007/s00440-023-01241-5
Guillaume Carlier, Alex Delalande, Quentin Merigot
{"title":"Quantitative stability of barycenters in the Wasserstein space","authors":"Guillaume Carlier, Alex Delalande, Quentin Merigot","doi":"10.1007/s00440-023-01241-5","DOIUrl":"https://doi.org/10.1007/s00440-023-01241-5","url":null,"abstract":"Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures of interest are often not accessible in their entirety and the practitioner may have to deal with statistical or computational approximations instead. In this article, we quantify the effect of such approximations on the corresponding barycenters. We show that Wasserstein barycenters depend in a Hölder-continuous way on their marginals under relatively mild assumptions. Our proof relies on recent estimates that allow to quantify the strong convexity of the barycenter functional. Consequences regarding the statistical estimation of Wasserstein barycenters and the convergence of regularized Wasserstein barycenters towards their non-regularized counterparts are explored.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"51 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters 非相容图上的微超临界渗流II:无限团簇的生长和等渗
1区 数学
Probability Theory and Related Fields Pub Date : 2023-10-17 DOI: 10.1007/s00440-023-01240-6
Tom Hutchcroft
{"title":"Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters","authors":"Tom Hutchcroft","doi":"10.1007/s00440-023-01240-6","DOIUrl":"https://doi.org/10.1007/s00440-023-01240-6","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the pitchfork bifurcation for the Chafee–Infante equation with additive noise 加性噪声下Chafee-Infante方程的干草叉分岔
1区 数学
Probability Theory and Related Fields Pub Date : 2023-10-05 DOI: 10.1007/s00440-023-01235-3
Alex Blumenthal, Maximilian Engel, Alexandra Neamtu
{"title":"On the pitchfork bifurcation for the Chafee–Infante equation with additive noise","authors":"Alex Blumenthal, Maximilian Engel, Alexandra Neamtu","doi":"10.1007/s00440-023-01235-3","DOIUrl":"https://doi.org/10.1007/s00440-023-01235-3","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134946884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise 输运噪声扰动下三维欧拉方程的全局存在性和非唯一性
1区 数学
Probability Theory and Related Fields Pub Date : 2023-10-03 DOI: 10.1007/s00440-023-01233-5
Martina Hofmanová, Theresa Lange, Umberto Pappalettera
{"title":"Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise","authors":"Martina Hofmanová, Theresa Lange, Umberto Pappalettera","doi":"10.1007/s00440-023-01233-5","DOIUrl":"https://doi.org/10.1007/s00440-023-01233-5","url":null,"abstract":"Abstract We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Hölder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow transformation reducing the SPDE under investigation to a random PDE, and convex integration techniques introduced in the deterministic setting by De Lellis and Székelyhidi, here adapted to consider the stochastic case. In particular, our novel approach allows to construct probabilistically strong solutions on $$[0,infty )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> directly.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Mesoscopic central limit theorem for non-Hermitian random matrices 非厄米随机矩阵的介观中心极限定理
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-28 DOI: 10.1007/s00440-023-01229-1
Giorgio Cipolloni, László Erdős, Dominik Schröder
{"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","authors":"Giorgio Cipolloni, László Erdős, Dominik Schröder","doi":"10.1007/s00440-023-01229-1","DOIUrl":"https://doi.org/10.1007/s00440-023-01229-1","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135387477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The random walk on upper triangular matrices over $$mathbb {Z}/m mathbb {Z}$$ 上三角矩阵上的随机游走 $$mathbb {Z}/m mathbb {Z}$$
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-27 DOI: 10.1007/s00440-023-01228-2
Evita Nestoridi, Allan Sly
{"title":"The random walk on upper triangular matrices over $$mathbb {Z}/m mathbb {Z}$$","authors":"Evita Nestoridi, Allan Sly","doi":"10.1007/s00440-023-01228-2","DOIUrl":"https://doi.org/10.1007/s00440-023-01228-2","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135471802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Stationary local random countable sets over the Wiener noise 维纳噪声上的平稳局部随机可数集
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-26 DOI: 10.1007/s00440-023-01227-3
Matija Vidmar, Jon Warren
{"title":"Stationary local random countable sets over the Wiener noise","authors":"Matija Vidmar, Jon Warren","doi":"10.1007/s00440-023-01227-3","DOIUrl":"https://doi.org/10.1007/s00440-023-01227-3","url":null,"abstract":"Abstract The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson’s question, whether or not there are any others, and develop some general theory for such sets. An extra ingredient to their structure, that of an honest indexation, leads to a splitting result that is akin to the Wiener–Hopf factorization of the Brownian motion at the minimum (or maximum) and has the latter as a special case. Sets admitting an honest indexation are moreover shown to have the property that no stopping time belongs to them with positive probability. They are also minimal: they do not have any non-empty proper local stationary subsets. Random sets, of the kind studied in this paper, honestly indexed or otherwise, give rise to nonclassical one-dimensional noises, generalizing the noise of splitting. Some properties of these noises and the inter-relations between them are investigated. In particular, subsets are connected to subnoises.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134960043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local law and rigidity for unitary Brownian motion 酉布朗运动的局部律和刚性
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-25 DOI: 10.1007/s00440-023-01230-8
Arka Adhikari, Benjamin Landon
{"title":"Local law and rigidity for unitary Brownian motion","authors":"Arka Adhikari, Benjamin Landon","doi":"10.1007/s00440-023-01230-8","DOIUrl":"https://doi.org/10.1007/s00440-023-01230-8","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Long lines in subsets of large measure in high dimension 高维大度量子集中的长线
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-22 DOI: 10.1007/s00440-023-01231-7
Dor Elboim, Bo’az Klartag
{"title":"Long lines in subsets of large measure in high dimension","authors":"Dor Elboim, Bo’az Klartag","doi":"10.1007/s00440-023-01231-7","DOIUrl":"https://doi.org/10.1007/s00440-023-01231-7","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Extremal singular values of random matrix products and Brownian motion on $$textsf {GL} (N,mathbb {C})$$ 随机矩阵积的极值奇异值与上的布朗运动 $$textsf {GL} (N,mathbb {C})$$
1区 数学
Probability Theory and Related Fields Pub Date : 2023-09-20 DOI: 10.1007/s00440-023-01217-5
Andrew Ahn
{"title":"Extremal singular values of random matrix products and Brownian motion on $$textsf {GL} (N,mathbb {C})$$","authors":"Andrew Ahn","doi":"10.1007/s00440-023-01217-5","DOIUrl":"https://doi.org/10.1007/s00440-023-01217-5","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136309013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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