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Correction: Sandwiching dense random regular graphs between binomial random graphs 更正:将密集随机正则图夹在二项随机图之间
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-08-01 DOI: 10.1007/s00440-023-01221-9
Pu Gao, M. Isaev, B. McKay
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引用次数: 3
Correction to: Asymptotic moments of spatial branching processes 修正：空间分支过程的渐近矩
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-07-21 DOI: 10.1007/s00440-023-01220-w
I. González, E. Horton, A. Kyprianou
{"title":"Correction to: Asymptotic moments of spatial branching processes","authors":"I. González, E. Horton, A. Kyprianou","doi":"10.1007/s00440-023-01220-w","DOIUrl":"https://doi.org/10.1007/s00440-023-01220-w","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"187 1","pages":"505 - 515"},"PeriodicalIF":2.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44513479","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
Correction to: Quenched large deviation principle for words in a letter sequence 更正：字母序列中单词的淬火大偏差原则
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-07-03 DOI: 10.1007/s00440-023-01212-w
M. Birkner, A. Greven, F. Hollander
{"title":"Correction to: Quenched large deviation principle for words in a letter sequence","authors":"M. Birkner, A. Greven, F. Hollander","doi":"10.1007/s00440-023-01212-w","DOIUrl":"https://doi.org/10.1007/s00440-023-01212-w","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"187 1","pages":"523 - 569"},"PeriodicalIF":2.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43978656","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
Correction: CLT in functional linear regression models 修正:函数线性回归模型中的CLT
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-06-23 DOI: 10.1007/s00440-023-01215-7
H. Cardot, André Mas, P. Sarda
{"title":"Correction: CLT in functional linear regression models","authors":"H. Cardot, André Mas, P. Sarda","doi":"10.1007/s00440-023-01215-7","DOIUrl":"https://doi.org/10.1007/s00440-023-01215-7","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"187 1","pages":"519 - 522"},"PeriodicalIF":2.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43593153","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
Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs 多尺度McKean–Vlasov SDE的中心极限型定理和大偏差原理
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-06-17 DOI: 10.1007/s00440-023-01214-8
Wei Hong, Shihu Li, Wei Liu, Xiaobin Sun
{"title":"Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs","authors":"Wei Hong, Shihu Li, Wei Liu, Xiaobin Sun","doi":"10.1007/s00440-023-01214-8","DOIUrl":"https://doi.org/10.1007/s00440-023-01214-8","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"187 1","pages":"133 - 201"},"PeriodicalIF":2.0,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46465484","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
On the $$Phi $$-stability and related conjectures 论$$Phi $$ -稳定性及相关猜想
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-05-12 DOI: 10.1007/s00440-023-01209-5
Lei Yu
{"title":"On the $$Phi $$-stability and related conjectures","authors":"Lei Yu","doi":"10.1007/s00440-023-01209-5","DOIUrl":"https://doi.org/10.1007/s00440-023-01209-5","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46411687","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
Random walks on $$textrm{SL}_2({mathbb {C}})$$: spectral gap and limit theorems $$textrm上的随机行走{SL}_2（｛mathbb｛C｝｝）$$：谱间隙和极限定理
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-02-10 DOI: 10.1007/s00440-023-01191-y
T. Dinh, Lucas Kaufmann, Hao-Yun Wu
{"title":"Random walks on $$textrm{SL}_2({mathbb {C}})$$: spectral gap and limit theorems","authors":"T. Dinh, Lucas Kaufmann, Hao-Yun Wu","doi":"10.1007/s00440-023-01191-y","DOIUrl":"https://doi.org/10.1007/s00440-023-01191-y","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45232832","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
Free boundary dimers: random walk representation and scaling limit. 自由边界二聚体：随机行走表示和缩放限制。
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-01-01 Epub Date: 2023-05-16 DOI: 10.1007/s00440-023-01203-x
Nathanaël Berestycki, Marcin Lis, Wei Qian
{"title":"Free boundary dimers: random walk representation and scaling limit.","authors":"Nathanaël Berestycki,&nbsp;Marcin Lis,&nbsp;Wei Qian","doi":"10.1007/s00440-023-01203-x","DOIUrl":"10.1007/s00440-023-01203-x","url":null,"abstract":"<p><p>We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight <math><mrow><mi>z</mi><mo>></mo><mn>0</mn></mrow></math> to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211-238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model describes a walk with transition weights that are negative along the free boundary. Yet under certain assumptions, which are in particular satisfied in the infinite volume limit in the upper half-plane, we prove an effective, true random walk representation for the inverse Kasteleyn matrix. In this case we further show that, independently of the value of <math><mrow><mi>z</mi><mo>></mo><mn>0</mn></mrow></math>, the scaling limit of the centered height function is the Gaussian free field with Neumann (or free) boundary conditions. It is the first example of a discrete model where such boundary conditions arise in the continuum scaling limit.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"186 3-4","pages":"735-812"},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10271954/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9654894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global solutions of aggregation equations and other flows with random diffusion. 聚合方程及其他随机扩散流动的全局解。
IF 1.5 1区 数学
Probability Theory and Related Fields Pub Date : 2023-01-01 Epub Date: 2022-10-31 DOI: 10.1007/s00440-022-01171-8
Matthew Rosenzweig, Gigliola Staffilani
{"title":"Global solutions of aggregation equations and other flows with random diffusion.","authors":"Matthew Rosenzweig, Gigliola Staffilani","doi":"10.1007/s00440-022-01171-8","DOIUrl":"10.1007/s00440-022-01171-8","url":null,"abstract":"<p><p>Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions with finite second moment can exist only locally in time. Nevertheless, one can ask whether global existence can be restored by adding a suitable noise to the equation, so that the dynamics are now stochastic. Inspired by the work of Buckmaster et al. (Int Math Res Not IMRN 23:9370-9385, 2020) showing that, with high probability, the inviscid SQG equation with random diffusion has global classical solutions, we investigate whether suitable random diffusion can restore global existence for a large class of active scalar equations in arbitrary dimension with possibly singular velocity fields. This class includes Hamiltonian flows, such as the SQG equation and its generalizations, and gradient flows, such as those arising in aggregation models. For this class, we show global existence of solutions in Gevrey-type Fourier-Lebesgue spaces with quantifiable high probability.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"185 3-4","pages":"1219-1262"},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10032336/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9546081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic Lorentz gas with small scatterers. 具有小散射体的周期洛伦兹气体。
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2023-01-01 Epub Date: 2023-03-15 DOI: 10.1007/s00440-023-01197-6
Péter Bálint, Henk Bruin, Dalia Terhesiu
{"title":"Periodic Lorentz gas with small scatterers.","authors":"Péter Bálint,&nbsp;Henk Bruin,&nbsp;Dalia Terhesiu","doi":"10.1007/s00440-023-01197-6","DOIUrl":"10.1007/s00440-023-01197-6","url":null,"abstract":"<p><p>We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time <i>n</i> tends to infinity, the scatterer size <math><mi>ρ</mi></math> may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well-studied regimes with superdiffusive <math><msqrt><mrow><mi>n</mi><mo>log</mo><mi>n</mi></mrow></msqrt></math> scaling (i) for fixed infinite horizon configurations-letting first <math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math> and then <math><mrow><mi>ρ</mi><mo>→</mo><mn>0</mn></mrow></math>-studied e.g. by Szász and Varjú (J Stat Phys 129(1):59-80, 2007) and (ii) Boltzmann-Grad type situations-letting first <math><mrow><mi>ρ</mi><mo>→</mo><mn>0</mn></mrow></math> and then <math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math>-studied by Marklof and Tóth (Commun Math Phys 347(3):933-981, 2016) .</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"186 1-2","pages":"159-219"},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10169905/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10296939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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