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The Scaling Limit of Random Two-Connected Series-Parallel Maps. 随机两连通串并联映射的标度极限。
IF 0.7 4区 数学
Journal of Theoretical Probability Pub Date : 2026-01-01 Epub Date: 2026-08-27 DOI: 10.1007/s10959-026-01537-x
Daniel Amankwah, Jakob Björnberg, Sigurdur Örn Stefánsson, Benedikt Stufler, Joonas Turunen
{"title":"The Scaling Limit of Random Two-Connected Series-Parallel Maps.","authors":"Daniel Amankwah, Jakob Björnberg, Sigurdur Örn Stefánsson, Benedikt Stufler, Joonas Turunen","doi":"10.1007/s10959-026-01537-x","DOIUrl":"https://doi.org/10.1007/s10959-026-01537-x","url":null,"abstract":"<p><p>A finite graph embedded in the plane is called a series-parallel map if it can be obtained from a finite tree by repeatedly subdividing and doubling edges. We study the scaling limit of weighted random two-connected series-parallel maps with <i>n</i> edges and show that under fairly general integrability conditions on these weights, the maps with distances rescaled by a factor <math><msup><mi>n</mi> <mrow><mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn></mrow> </msup> </math> converge to a constant multiple of Aldous' continuum random tree (CRT) in the Gromov-Hausdorff sense. The proof relies on a bijection between a set of trees with <i>n</i> leaves and a set of series-parallel maps with <i>n</i> edges, together with a novel <i>blob decomposition</i> of the maps.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"39 4","pages":"75"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13522014/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148851155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Second-Class Particle in the Half-Line Open Totally Asymmetric Simple Exclusion Process. 半线开放完全不对称简单不相容过程中的第二类粒子。
IF 0.7 4区 数学
Journal of Theoretical Probability Pub Date : 2026-01-01 Epub Date: 2026-09-09 DOI: 10.1007/s10959-026-01544-y
Kailun Chen
{"title":"The Second-Class Particle in the Half-Line Open Totally Asymmetric Simple Exclusion Process.","authors":"Kailun Chen","doi":"10.1007/s10959-026-01544-y","DOIUrl":"https://doi.org/10.1007/s10959-026-01544-y","url":null,"abstract":"<p><p>We consider the second-class particle in half-line open totally asymmetric exclusion process (TASEP) under two different initial conditions with shock discontinuities. The exact formulas for the distribution of the second-class particle can be derived by using the color-position symmetry theorem of colored half-space TASEP. We study the asymptotic distributions of second-class particles under the constant scaling and Kardar-Parisi-Zhang-type scaling.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"39 4","pages":"84"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13558387/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148931931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Invariance Principle for Lifts of Geodesic Random Walks. 测地线随机漫步提升的不变性原理。
IF 0.6 4区 数学
Journal of Theoretical Probability Pub Date : 2026-01-01 Epub Date: 2026-02-23 DOI: 10.1007/s10959-026-01480-x
Jonathan Junné, Frank Redig, Rik Versendaal
{"title":"Invariance Principle for Lifts of Geodesic Random Walks.","authors":"Jonathan Junné, Frank Redig, Rik Versendaal","doi":"10.1007/s10959-026-01480-x","DOIUrl":"https://doi.org/10.1007/s10959-026-01480-x","url":null,"abstract":"<p><p>We consider a certain class of Riemannian submersions <math><mrow><mi>π</mi> <mo>:</mo> <mi>N</mi> <mo>→</mo> <mi>M</mi></mrow> </math> and study lifted geodesic random walks from the base manifold <i>M</i> to the total manifold <i>N</i>. Under appropriate conditions on the distribution of the speed of the geodesic random walks, we prove an invariance principle, i.e., convergence to horizontal Brownian motion for the lifted walks. This gives us a natural probabilistic proof of the geometric identity relating the horizontal Laplacian <math><msub><mi>Δ</mi> <mi>H</mi></msub> </math> on <i>N</i> and the Laplace-Beltrami operator <math><msub><mi>Δ</mi> <mi>M</mi></msub> </math> on <i>M</i>. In the setting where <i>N</i> is the orthonormal frame bundle <i>O</i>(<i>M</i>), this identity is central in the Malliavin-Eells-Elworthy construction of Riemannian Brownian motion.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"39 2","pages":"21"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12929317/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147312526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Peierls Bounds from Toom Contours. 佩尔斯边界从空间轮廓。
IF 0.7 4区 数学
Journal of Theoretical Probability Pub Date : 2026-01-01 Epub Date: 2026-05-11 DOI: 10.1007/s10959-026-01508-2
Jan M Swart, Réka Szabó, Cristina Toninelli
{"title":"Peierls Bounds from Toom Contours.","authors":"Jan M Swart, Réka Szabó, Cristina Toninelli","doi":"10.1007/s10959-026-01508-2","DOIUrl":"10.1007/s10959-026-01508-2","url":null,"abstract":"<p><p>For deterministic monotone cellular automata on the <i>d</i>-dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. The proof of sufficiency is based on an intricate Peierls argument. We present a simplified version of this Peierls argument. Our main motivation is the open problem of determining stability of monotone cellular automata with intrinsic randomness, in which for the unperturbed evolution the local update rules at different space-time points are chosen in an i.i.d. fashion according to some fixed law. We apply Toom's Peierls argument to prove stability of a class of cellular automata with intrinsic randomness and also derive lower bounds on the critical parameter for some deterministic cellular automata.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"39 3","pages":"45"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13161273/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147935504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Law of Large Numbers for Local Patterns in Schur Measures and a Schur Process. 舒尔测度中局部模式的大数定律和舒尔过程。
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2025-01-01 Epub Date: 2025-06-02 DOI: 10.1007/s10959-025-01421-0
Pierre Lazag
{"title":"A Law of Large Numbers for Local Patterns in Schur Measures and a Schur Process.","authors":"Pierre Lazag","doi":"10.1007/s10959-025-01421-0","DOIUrl":"https://doi.org/10.1007/s10959-025-01421-0","url":null,"abstract":"<p><p>The aim of this note is to prove a law of large numbers for local patterns in discrete point processes. We investigate two different situations: a class of point processes on the one-dimensional lattice including certain Schur measures, and a model of random plane partitions, introduced by Okounkov and Reshetikhin. The results state in both cases that the linear statistic of a function, weighted by the appearance of a fixed pattern in the random configuration and conveniently normalized, converges to the deterministic integral of that function weighted by the expectation with respect to the limit process of the appearance of the pattern.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"38 3","pages":"56"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12130167/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144227688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Spine of Two-Particle Fleming-Viot Process in a Bounded Interval. 有界区间内两粒子Fleming-Viot过程的脊。
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2025-01-01 Epub Date: 2025-02-06 DOI: 10.1007/s10959-025-01401-4
Krzysztof Burdzy, János Engländer, Donald E Marshall
{"title":"The Spine of Two-Particle Fleming-Viot Process in a Bounded Interval.","authors":"Krzysztof Burdzy, János Engländer, Donald E Marshall","doi":"10.1007/s10959-025-01401-4","DOIUrl":"https://doi.org/10.1007/s10959-025-01401-4","url":null,"abstract":"<p><p>We show that the spine of the Fleming-Viot process driven by Brownian motion and starting with two particles in a bounded interval has a different law from that of Brownian motion conditioned to stay in the interval forever. Furthermore, we estimate the \"extra drift.\"</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"38 2","pages":"31"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11802667/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143384128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fractional Kolmogorov Equations with Singular Paracontrolled Terminal Conditions. 具有奇异傍控终端条件的分数阶Kolmogorov方程。
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2025-01-01 Epub Date: 2025-03-06 DOI: 10.1007/s10959-025-01408-x
Helena Kremp, Nicolas Perkowski
{"title":"Fractional Kolmogorov Equations with Singular Paracontrolled Terminal Conditions.","authors":"Helena Kremp, Nicolas Perkowski","doi":"10.1007/s10959-025-01408-x","DOIUrl":"10.1007/s10959-025-01408-x","url":null,"abstract":"<p><p>We consider backward fractional Kolmogorov equations with singular Besov drift of low regularity and singular terminal conditions. To treat drifts beyond the so-called Young regime, we assume an enhancement assumption on the drift and consider paracontrolled terminal conditions. Our work generalizes previous results on the equation from Cannizzaro and Chouk (Ann Probab 46:1710-1763, 2018), Kremp and Perkowski (Bernoulli 28:1757-1783, 2022. 10.3150/21-BEJ1394) to the case of <i>singular paracontrolled terminal conditions</i> and simultaneously treats singular and non-singular data in one concise solution theory. We introduce a paracontrolled solution space that implies parabolic time and space regularity on the solution without introducing the so-called modified paraproduct from Gubinelli and Perkowski (Commun Math Phys 349:165-269, 2017). The tools developed in this article apply for general linear PDEs that can be tackled with the paracontrolled ansatz.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"38 2","pages":"39"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11885396/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143588236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Positive Reinforced Generalized Time-Dependent Pólya Urns via Stochastic Approximation 通过随机逼近实现正向强化的广义时变波利亚乌恩
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-09-04 DOI: 10.1007/s10959-024-01366-w
Wioletta M. Ruszel, Debleena Thacker
{"title":"Positive Reinforced Generalized Time-Dependent Pólya Urns via Stochastic Approximation","authors":"Wioletta M. Ruszel, Debleena Thacker","doi":"10.1007/s10959-024-01366-w","DOIUrl":"https://doi.org/10.1007/s10959-024-01366-w","url":null,"abstract":"<p>Consider a generalized time-dependent Pólya urn process defined as follows. Let <span>(din mathbb {N})</span> be the number of urns/colors. At each time <i>n</i>, we distribute <span>(sigma _n)</span> balls randomly to the <i>d</i> urns, proportionally to <i>f</i>, where <i>f</i> is a valid reinforcement function. We consider a general class of positive reinforcement functions <span>(mathcal {R})</span> assuming some monotonicity and growth condition. The class <span>(mathcal {R})</span> includes convex functions and the classical case <span>(f(x)=x^{alpha })</span>, <span>(alpha &gt;1)</span>. The novelty of the paper lies in extending stochastic approximation techniques to the <i>d</i>-dimensional case and proving that eventually the process will fixate at some random urn and the other urns will not receive any balls anymore.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Invariant Measures for Stochastic Reaction–Diffusion Problems on Unbounded Thin Domains Driven by Nonlinear Noise 非线性噪声驱动的无界薄域上随机反应-扩散问题的不变度量
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-09-02 DOI: 10.1007/s10959-024-01367-9
Zhe Pu, Jianxiu Guo, Dingshi Li
{"title":"Invariant Measures for Stochastic Reaction–Diffusion Problems on Unbounded Thin Domains Driven by Nonlinear Noise","authors":"Zhe Pu, Jianxiu Guo, Dingshi Li","doi":"10.1007/s10959-024-01367-9","DOIUrl":"https://doi.org/10.1007/s10959-024-01367-9","url":null,"abstract":"<p>This article is concerned with the limiting behavior of invariant measures for stochastic reaction–diffusion equations driven by nonlinear noise on unbounded thin domains. We first show the existence of invariant measures when the diffusion terms are globally Lipschitz continuous. The uniform estimates on the tails of solutions are employed to present the tightness of a family of probability distributions of solutions in order to overcome the non-compactness of usual Sobolev embeddings on unbounded domains. Then, we prove any limit of invariant measures of the equations defined on <span>((n+1))</span>-dimensional unbounded thin domains must be an invariant measure of the limiting system as the thin domains collapse onto the space <span>(mathbb {R}^n)</span>.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Urns with Multiple Drawings and Graph-Based Interaction 带有多幅图画和基于图形的互动的骨灰瓮
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-08-22 DOI: 10.1007/s10959-024-01365-x
Yogesh Dahiya, Neeraja Sahasrabudhe
{"title":"Urns with Multiple Drawings and Graph-Based Interaction","authors":"Yogesh Dahiya, Neeraja Sahasrabudhe","doi":"10.1007/s10959-024-01365-x","DOIUrl":"https://doi.org/10.1007/s10959-024-01365-x","url":null,"abstract":"<p>Consider a finite undirected graph and place an urn with balls of two colours at each vertex. At every discrete time step, for each urn, a fixed number of balls are drawn from that same urn with probability <i>p</i> and from a randomly chosen neighbour of that urn with probability <span>(1-p)</span>. Based on what is drawn, the urns then reinforce themselves or their neighbours. For every ball of a given colour in the sample, in case of Pólya-type reinforcement, a constant multiple of balls of that colour is added while in case of Friedman-type reinforcement, balls of the other colour are reinforced. These different choices for reinforcement give rise to multiple models. In this paper, we study the convergence of the fraction of balls of either colour across urns for all of these models. We show that in most cases the urns synchronize, that is, the fraction of balls of either colour in each urn converges to the same limit almost surely. A different kind of asymptotic behaviour is observed on bipartite graphs. We also prove similar results for the case of finite directed graphs.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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