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Limit Theorems for Product of Spatial Average of Parabolic Anderson Model 抛物型Anderson模型空间平均积的极限定理
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4216-8
Jingyu Li, Yong Zhang, Zhiqiang Tang
{"title":"Limit Theorems for Product of Spatial Average of Parabolic Anderson Model","authors":"Jingyu Li,&nbsp;Yong Zhang,&nbsp;Zhiqiang Tang","doi":"10.1007/s10114-026-4216-8","DOIUrl":"10.1007/s10114-026-4216-8","url":null,"abstract":"<div><p>Let <i>u</i>(<i>t, x</i>) be the solution to the parabolic Anderson model on ℝ<sub>+</sub> × ℝ driven by a space-time white Gaussian noise. In this paper, we prove the central limit theorem and almost sure central limit theorem for product of spatial average of the form <span>(prodnolimits_{k=1}^{n} S_k)</span> as <i>n</i> → ∞ for fixed <i>t</i> &gt; 0, where <span>(S_k = int_{0}^{k} u(t, x)dx)</span>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1727 - 1741"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Saturated Set of One-dimensional Maps with Some Hyperbolicity 关于具有双曲性的一维映射的饱和集
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4523-0
Cao Zhao
{"title":"On the Saturated Set of One-dimensional Maps with Some Hyperbolicity","authors":"Cao Zhao","doi":"10.1007/s10114-026-4523-0","DOIUrl":"10.1007/s10114-026-4523-0","url":null,"abstract":"<div><p>The paper is mainly concerned with the multifractal analysis for smooth dynamical systems in dimension one without uniform hyperbolicity. We characterize the Hausdorff dimension of the saturated set obtained from the empirical measure by the local dimensions of hyperbolic measures for a topologically mixing <i>C</i><sup>2</sup> map modeled by an abstract dynamical system.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1755 - 1767"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Residual Monge–Ampère Mass and the Schwarz Symmetrization of Plurisubharmonic Functions 多次谐波函数的剩余monge - ampantere质量和Schwarz对称性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-5624-5
Xiaoman Duan, Yaoyao Hu, Liyou Zhang
{"title":"The Residual Monge–Ampère Mass and the Schwarz Symmetrization of Plurisubharmonic Functions","authors":"Xiaoman Duan,&nbsp;Yaoyao Hu,&nbsp;Liyou Zhang","doi":"10.1007/s10114-026-5624-5","DOIUrl":"10.1007/s10114-026-5624-5","url":null,"abstract":"<div><p>The aim of this paper is twofold. First, we prove that the Schwarz symmetrization does not increase the residual Monge–Ampère mass for circular invariant plurisubharmonic functions on balanced domains, confirming a conjecture of L. Li. Second, we prove that the Schwarz symmetrization preserves plurisubharmonicity for all quasi-circular invariant plurisubharmonic functions. Consequently, we show that the Schwarz symmetrization does not increase the Monge–Ampère energy in this case. As an application, we obtain the sharp Moser–Trudinger inequality for quasi-circular invariant plurisubharmonic functions, which generalizes a previous result by Berman and Berndtsson. Finally, we construct explicit examples demonstrating the lack of uniform comparisons for higher-order Lelong numbers under the Schwarz symmetrization.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2000 - 2024"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
One Note on n-Sensitivity in Mean Forms 关于均值形式n灵敏度的一个注意事项
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4584-0
Zhongxuan Yang, Xiaojun Huang
{"title":"One Note on n-Sensitivity in Mean Forms","authors":"Zhongxuan Yang,&nbsp;Xiaojun Huang","doi":"10.1007/s10114-026-4584-0","DOIUrl":"10.1007/s10114-026-4584-0","url":null,"abstract":"<div><p>In 2022, Li, Ye and Yu introduced multivariate sensitivity version of notions of mean <i>m</i>-Sensitivity and <i>m</i>-sensitivity in the mean for <i>m</i> ≥ 2. In this manuscript, we mainly focus on the investigation of multivariate sensitivity in mean forms. First, we prove that for a linear system, the equivalence between mean <i>m</i>-sensitivity and <i>m</i>-sensitivity in the mean holds without any more conditions. Subsequently, we introduce the notion of <i>m</i>-equicontinuity in the mean, and obtain an Auslander–Yorke type dichotomy between <i>m</i>-equicontinuity in the mean and <i>m</i>-sensitivity in the mean for minimal systems. As a consequence, we demonstrate that the equivalence between mean <i>m</i>-sensitivity and <i>m</i>-sensitivity in the mean is valid under the condition of minimality for a general system, thereby affirmatively resolving the conjecture proposed in [Li, J., Ye, X. D., Yu, T.: Equicontinuity and sensitivity in mean forms. <i>J. Dynam. Differential Equations</i>, <b>34</b>, 133–154 (2022)].</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1869 - 1880"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Legendrian Submanifolds of (mathbb{S}^{2n+1}(tilde{c})) with Constant Sectional Curvature and Conformal Maslov Form 具有常截面曲率和保形马斯洛夫形式的(mathbb{S}^{2n+1}(tilde{c}))的legendri子流形
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-5075-z
Xiuxiu Cheng, Qian Li, Zejun Hu
{"title":"Legendrian Submanifolds of (mathbb{S}^{2n+1}(tilde{c})) with Constant Sectional Curvature and Conformal Maslov Form","authors":"Xiuxiu Cheng,&nbsp;Qian Li,&nbsp;Zejun Hu","doi":"10.1007/s10114-026-5075-z","DOIUrl":"10.1007/s10114-026-5075-z","url":null,"abstract":"<div><p>In this paper, we study Legendrian submanifolds of the Sasakian space form <span>(mathbb{S}^{2n+1}(tilde{c}))</span> with constant sectional curvature and conformal Maslov form. As main results, we first classify the 2-dimensional Legendrian submanifolds of <span>(mathbb{S}^{5}(tilde{c}))</span> with constant sectional curvature and conformal Maslov form; then we establish a complete classification of the Legendrian submanifolds of <span>(mathbb{S}^{2n+1}(tilde{c}))</span> with constant sectional curvature and <i>C</i>-parallel mean curvature vector field.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1899 - 1920"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Relationship Between Meromorphic Functions with Three IM Sharing Values and One CM Sharing Value 具有三个IM共享值和一个CM共享值的亚纯函数之间的关系
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4474-5
Lan Hu, Min Su, Yuhua Li
{"title":"The Relationship Between Meromorphic Functions with Three IM Sharing Values and One CM Sharing Value","authors":"Lan Hu,&nbsp;Min Su,&nbsp;Yuhua Li","doi":"10.1007/s10114-026-4474-5","DOIUrl":"10.1007/s10114-026-4474-5","url":null,"abstract":"<div><p>In this paper, we investigate the uniqueness of meromorphic functions sharing four values. We show that if <i>f</i>(<i>z</i>) and <i>g</i>(<i>z</i>) are distinct non-constant meromorphic functions sharing 0, 1, <i>c</i> IM and ∞ CM, then either <i>f</i>(<i>z</i>) and <i>g</i>(<i>z</i>) share 0, 1, <i>c</i>, ∞ CM or <span>(frac{1}{13} T(r, f) - 2bar{N}(r, f) leq N_{E}^{(1)}(r, 0) + N_{E}^{(1)}(r, 1) + N_{E}^{(1)}(r, c) + S(r, f) leq frac{4}{3} T(r, f) - frac{2}{3} bar{N}(r, f))</span> holds.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1742 - 1754"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Preface of the Special Issue on Discrete Probability and Mathematical Physics 离散概率与数学物理专刊前言
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-16 DOI: 10.1007/s10114-026-5640-5
Zhen-Qing Chen, Jian Ding, Fuzhou Gong, Zhiming Ma, Zhan Shi, Hao Wu
{"title":"Preface of the Special Issue on Discrete Probability and Mathematical Physics","authors":"Zhen-Qing Chen,&nbsp;Jian Ding,&nbsp;Fuzhou Gong,&nbsp;Zhiming Ma,&nbsp;Zhan Shi,&nbsp;Hao Wu","doi":"10.1007/s10114-026-5640-5","DOIUrl":"10.1007/s10114-026-5640-5","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1431 - 1431"},"PeriodicalIF":0.9,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Large Deviations at the Origin of Random Walk in Random Environment 随机环境下随机行走起源处的大偏差
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4531-0
Alexander Drewitz, Alejandro Ramírez, Santiago Saglietti, Zhicheng Zheng
{"title":"Large Deviations at the Origin of Random Walk in Random Environment","authors":"Alexander Drewitz,&nbsp;Alejandro Ramírez,&nbsp;Santiago Saglietti,&nbsp;Zhicheng Zheng","doi":"10.1007/s10114-026-4531-0","DOIUrl":"10.1007/s10114-026-4531-0","url":null,"abstract":"<div><p>We consider a random walk in an independent and identically distributed (i.i.d.) random environment on ℤ<sup><i>d</i></sup> and study properties of its large deviation rate function at the origin. It was proved by Comets, Gantert and Zeitouni in dimension <i>d</i> = 1 in 1999 and later by Varadhan in dimensions <i>d</i> ≥ 2 in 2003 that, for uniformly elliptic i.i.d. random environments, the quenched and the averaged large deviation rate functions coincide at the origin. Here we provide a description of an atypical event realizing the correct quenched large deviation rate in the nestling and marginally nestling setting: the random walk seeks regions of space where the environment emulates the element in the convex hull of the support of the law of the environment at a site which minimizes the rate function. Periodic environments play a natural role in this description.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1662 - 1684"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Intermediate Level-sets of the Four-dimensional Membrane Model 四维膜模型的中间水平集
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4341-4
Xinyi Li, Runsheng Liu
{"title":"The Intermediate Level-sets of the Four-dimensional Membrane Model","authors":"Xinyi Li,&nbsp;Runsheng Liu","doi":"10.1007/s10114-026-4341-4","DOIUrl":"10.1007/s10114-026-4341-4","url":null,"abstract":"<div><p>In this paper, we consider the discrete membrane model in four dimensions. We confirm the existence of the scaling limit of the intermediate (i.e., a multiple of the expected maximum) level-sets of the model, and show that it is equal in law to a tilted version of the sub-critical Gaussian multiplicative chaos (GMC) measure of the continuum membrane model.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1432 - 1456"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Size Distribution of Clusters in Site-percolation on Random Recursive Tree 随机递归树上点渗簇的大小分布
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4437-x
Chenlin Gu, Linglong Yuan
{"title":"Size Distribution of Clusters in Site-percolation on Random Recursive Tree","authors":"Chenlin Gu,&nbsp;Linglong Yuan","doi":"10.1007/s10114-026-4437-x","DOIUrl":"10.1007/s10114-026-4437-x","url":null,"abstract":"<div><p>We prove rigorously several results about the site-percolation on random recursive trees, observed in the previous work by Kalay and Ben–Naim (<i>J. Phys. A.</i>, 2015). For a random recursive tree of size <i>n</i>, let every site have probability <i>p</i> ∈ (0, 1) to remain and with probability (1 − <i>p</i>) to be removed. As <i>n</i> → ∞, we show that the proportion of the remaining clusters of size <i>k</i> is of order <span>(k^{-1-{1over{p}}})</span>, resulting in a Yule–Simon distribution; the largest cluster size is of order <i>n</i><sup><i>p</i></sup>, and admits a non-trivial scaling limit. The proofs are based on the embedding of this model in the multi-type branching processes, and a coupling with the bond-percolation on random recursive trees.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1572 - 1594"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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