Probability Theory and Related Fields最新文献

Dissipative particle systems on expanders. 膨胀机上的耗散粒子系统。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2025-05-19 DOI: 10.1007/s00440-025-01383-8

John Haslegrave, Peter Keevash

引用次数: 0

Weak convergence of stochastic integrals on Skorokhod space in Skorokhod's J 1 and M 1 topologies. Skorokhod j1和m1拓扑下Skorokhod空间上随机积分的弱收敛性。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2026-03-23 DOI: 10.1007/s00440-026-01476-y

Andreas Søjmark, Fabrice Wunderlich

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Weak convergence of stochastic integrals on Skorokhod space in Skorokhod's <ns0:math><ns0:msub><ns0:mi>J</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msub> </ns0:math> and <ns0:math><ns0:msub><ns0:mi>M</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msub> </ns0:math> topologies.","authors":"Andreas Søjmark, Fabrice Wunderlich","doi":"10.1007/s00440-026-01476-y","DOIUrl":"10.1007/s00440-026-01476-y","url":null,"abstract":"We provide criteria for Itô integration to behave continuously with respect to Skorokhod's <math><msub><mi>J</mi> <mn>1</mn></msub> </math> and <math><msub><mi>M</mi> <mn>1</mn></msub> </math> topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the <math><msub><mi>M</mi> <mn>1</mn></msub> </math> setting and unify existing theories in the <math><msub><mi>J</mi> <mn>1</mn></msub> </math> case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, <math><msub><mi>M</mi> <mn>1</mn></msub> </math> tightness in fact implies <math><msub><mi>J</mi> <mn>1</mn></msub> </math> tightness under a mild localised uniform integrability condition. Finally, we apply our results to study scaling limits of models of anomalous diffusion driven by continuous-time random walks. This yields new results on weak <math><msub><mi>M</mi> <mn>1</mn></msub> </math> and <math><msub><mi>J</mi> <mn>1</mn></msub> </math> convergence to stochastic integrals against subordinated stable processes. In the case of superdiffusive scaling, an interesting counterexample is obtained.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"195 3-4","pages":"997-1049"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13503488/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148819337","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

Regularisation by multiplicative noise for reaction-diffusion equations. 反应扩散方程的乘性噪声正则化。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2026-03-07 DOI: 10.1007/s00440-026-01474-0

Konstantinos Dareiotis, Teodor Holland, Khoa Lê

引用次数: 0

An invariance principle for the 2d weakly self-repelling Brownian polymer. 二维弱自排斥布朗聚合物的不变性原理。

IF 1.6 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2025-02-14 DOI: 10.1007/s00440-025-01363-y

Giuseppe Cannizzaro, Harry Giles

{"title":"An invariance principle for the 2d weakly self-repelling Brownian polymer.","authors":"Giuseppe Cannizzaro, Harry Giles","doi":"10.1007/s00440-025-01363-y","DOIUrl":"https://doi.org/10.1007/s00440-025-01363-y","url":null,"abstract":"We investigate the large-scale behaviour of the Self-Repelling Brownian Polymer (SRBP) in the critical dimension <math><mrow><mi>d</mi> <mo>=</mo> <mn>2</mn></mrow> </math> . The SRBP is a model of self-repelling motion, which is formally given by the solution to a stochastic differential equation driven by a standard Brownian motion and with a drift given by the negative gradient of its own local time. As with its discrete counterpart, the \"true\" self-avoiding walk (TSAW) of Amit et al. (Phys Rev B 27(3):1635-1645, 1983. 10.1103/PhysRevB.27.1635), it is conjectured to be logarithmically superdiffusive, i.e. to be such that its mean-square displacement grows as <math><mrow><mi>t</mi> <msup><mrow><mo>(</mo> <mo>log</mo> <mi>t</mi> <mo>)</mo></mrow> <mi>β</mi></msup> </mrow> </math> for t large and some currently unknown <math><mrow><mi>β</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></mrow> </math> . The main result of the paper is an invariance principle for the SRBP under the weak coupling scaling, which corresponds to scaling the SRBP diffusively and simultaneously tuning down the strength of the self-interaction in a scale-dependent way. The diffusivity for the limiting Brownian motion is explicit and its expression provides compelling evidence that the <math><mi>β</mi></math> above should be 1/2. Further, we derive the scaling limit of the so-called environment seen by the particle process, which formally solves a non-linear singular stochastic PDE of transport-type, and prove this is given by the solution of a stochastic linear transport equation with enhanced diffusivity.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"194 1-2","pages":"411-483"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12929435/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147309453","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

Gaussian Correlation via Inverse Brascamp-Lieb. 基于逆Brascamp-Lieb的高斯相关。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2025-11-13 DOI: 10.1007/s00440-025-01445-x

Emanuel Milman

引用次数: 0

Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits. 特殊随机标度极限下被动标量和矢量平流方程的Vlasov方程和Young测度。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2026-04-10 DOI: 10.1007/s00440-026-01471-3

Federico Butori, Franco Flandoli, Eliseo Luongo, Yassine Tahraoui

引用次数: 0

Tip growth in a strongly concentrated conformal growth model follows local geodesics. 在强集中的保形生长模型中，尖端生长遵循局部测地线。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2026-05-21 DOI: 10.1007/s00440-026-01494-w

Frankie Higgs

{"title":"Tip growth in a strongly concentrated conformal growth model follows local geodesics.","authors":"Frankie Higgs","doi":"10.1007/s00440-026-01494-w","DOIUrl":"10.1007/s00440-026-01494-w","url":null,"abstract":"We analyse the aggregate Loewner evolution (ALE), introduced in 2018 by Sola, Turner and Viklund to generalise versions of diffusion limited aggregation (DLA) in the plane using complex analysis. They showed convergence of the ALE for certain parameters to a single growing slit. Started from a non-trivial initial configuration of k needles and the same parameters, we show that the small-particle scaling limit of ALE is the Laplacian path model, introduced by Carleson and Makarov, in which the tips grow along geodesics towards <math><mi>∞</mi></math> . Our proof involves analysis of Loewner's equation near its singular points, and we extend martingale methods to the backward equation, where what we have to control is non-adapted. Most conformal growth models introduce an extra regularisation factor to deal with the singularities in Loewner's equation at the sharp tips and right-angle bases of slit particles. As an intermediate step we prove a limit result for a model with no such regularisation factor, developing methods which should prove useful in analysing other weakly-regularised models with non-trivial limits.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"196 3-4","pages":"2031-2084"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13672436/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149216085","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

Mixing of fast random walks on dynamic random permutations. 动态随机排列上快速随机行走的混合。

IF 1.6 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2025-04-24 DOI: 10.1007/s00440-025-01375-8

Luca Avena, Remco van der Hofstad, Frank den Hollander, Oliver Nagy

引用次数: 0

Decorrelation transition in the Wigner minor process. 维格纳小过程中的去相关转换。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2025-09-20 DOI: 10.1007/s00440-025-01422-4

Zhigang Bao, Giorgio Cipolloni, László Erdős, Joscha Henheik, Oleksii Kolupaiev

{"title":"Decorrelation transition in the Wigner minor process.","authors":"Zhigang Bao, Giorgio Cipolloni, László Erdős, Joscha Henheik, Oleksii Kolupaiev","doi":"10.1007/s00440-025-01422-4","DOIUrl":"10.1007/s00440-025-01422-4","url":null,"abstract":"We consider the Wigner minor process, i.e. the eigenvalues of an <math><mrow><mi>N</mi> <mo>×</mo> <mi>N</mi></mrow> </math> Wigner matrix <math><msup><mi>H</mi> <mrow><mo>(</mo> <mi>N</mi> <mo>)</mo></mrow> </msup> </math> together with the eigenvalues of all its <math><mrow><mi>n</mi> <mo>×</mo> <mi>n</mi></mrow> </math> minors, <math><msup><mi>H</mi> <mrow><mo>(</mo> <mi>n</mi> <mo>)</mo></mrow> </msup> </math> , <math><mrow><mi>n</mi> <mo>≤</mo> <mi>N</mi></mrow> </math> . The top eigenvalues of <math><msup><mi>H</mi> <mrow><mo>(</mo> <mi>N</mi> <mo>)</mo></mrow> </msup> </math> and those of its immediate minor <math><msup><mi>H</mi> <mrow><mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> </msup> </math> are very strongly correlated, but this correlation becomes weaker for smaller minors <math><msup><mi>H</mi> <mrow><mo>(</mo> <mi>N</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo></mrow> </msup> </math> as k increases. For the GUE minor process the critical transition regime around <math><mrow><mi>k</mi> <mo>∼</mo> <msup><mi>N</mi> <mrow><mn>2</mn> <mo>/</mo> <mn>3</mn></mrow> </msup> </mrow> </math> was analyzed by Forrester and Nagao (Forrester and Nagao, J. Stat. Mech. (08): P08011, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"196 3-4","pages":"1075-1126"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13672449/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149216663","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

Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions. 高斯Weyl-Heisenberg函数零点的超均匀性和非超均匀性。

IF 1.9 1区数学

Probability Theory and Related Fields Pub Date : 2026-01-01 Epub Date: 2026-06-27 DOI: 10.1007/s00440-026-01512-x

Naomi Feldheim, Antti Haimi, Günther Koliander, José Luis Romero

{"title":"Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions.","authors":"Naomi Feldheim, Antti Haimi, Günther Koliander, José Luis Romero","doi":"10.1007/s00440-026-01512-x","DOIUrl":"10.1007/s00440-026-01512-x","url":null,"abstract":"We study zero sets of twisted stationary Gaussian random functions on the complex plane, i.e., Gaussian random functions that are stochastically invariant under the action of the Weyl-Heisenberg group. This model includes translation-invariant Gaussian entire functions (GEFs), and also many other non-analytic examples, in which case winding numbers around zeros can be either positive or negative. We investigate zero statistics both when zeros are weighted with their winding numbers (charged zero set) and when they are not (uncharged zero set). We show that the variance of the charged zero statistic always grows linearly with the radius of the observation disk (hyperuniformity). Importantly, this holds for functions with possibly non-zero means and without assuming additional symmetries such as radiality. With respect to uncharged zero statistics, we provide an example for which the variance grows with the area of the observation disk (non-hyperuniformity). This is used to show that, while the zeros of GEFs are hyperuniform, the set of their critical points fails to be so. Our work contributes to recent developments in statistical signal processing, where the time-frequency profile of a non-stationary signal embedded into noise is revealed by performing a statistical test on the zeros of its spectrogram (\"silent points\"). We show that empirical spectrogram zero counts enjoy moderate deviations from their ensemble averages over large observation windows (something that was previously known only for pure noise). In contrast, we also show that spectrogram maxima (\"loud points\") fail to enjoy a similar property. This gives the first formal evidence for the statistical superiority of silent points over the competing feature of loud points, a fact that has been noted by practitioners. In the same vein, our second order asymptotics for spectrogram maxima show that certain heuristic proxy models used in signal processing are inaccurate at large scales.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"195 3-4","pages":"1699-1764"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13503458/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148819312","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