发布求助
文献互助 智能选刊 最新文献

Acta Mathematica Sinica-English Series最新文献

筛选
英文 中文
Boundedness of Discounted Tree Sums 贴现树和的有界性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4459-4
Elie Aïdékon, Yueyun Hu, Zhan Shi
{"title":"Boundedness of Discounted Tree Sums","authors":"Elie Aïdékon,&nbsp;Yueyun Hu,&nbsp;Zhan Shi","doi":"10.1007/s10114-026-4459-4","DOIUrl":"10.1007/s10114-026-4459-4","url":null,"abstract":"<div><p>Let <span>((V(u), uin {cal{T}}))</span> be a (supercritical) branching random walk and <span>((eta_{u}, uin {cal{T}}))</span> be marks on the vertices of the tree, distributed in an i.i.d. fashion. Following Aldous and Bandyopadhyay [<i>Ann. Appl. Probab.</i>, <b>15</b>, 1047–1110 (2005)], for each ray <i>ξ</i> of the tree, we associate the <i>discounted tree sum D</i>(<i>ξ</i>) which is the sum of the <span>(rm{e}^{-V(u)}eta_{u})</span> taken along the ray. The paper deals with the finiteness of sup<sub><i>ξ</i></sub><i>D</i>(<i>ξ</i>). To this end, we study the extreme behaviour of the local time processes of the paths (<i>V</i>(<i>u</i>), <i>u</i> ∈ <i>ξ</i>). It answers a question of Nicolas Curien, and partially solves Open Problem 31 of Aldous and Bandyopadhyay [<i>Ann. Appl. Probab.</i>, <b>15</b>, 1047–1110 (2005)]. We also present several open questions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1639 - 1661"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261759","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 for the Extremal Eigenvalues of Ginibre Ensembles Ginibre系综极值特征值的大偏差
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4382-8
Yuanyuan Xu, Qiang Zeng
{"title":"Large Deviations for the Extremal Eigenvalues of Ginibre Ensembles","authors":"Yuanyuan Xu,&nbsp;Qiang Zeng","doi":"10.1007/s10114-026-4382-8","DOIUrl":"10.1007/s10114-026-4382-8","url":null,"abstract":"<div><p>We establish large deviation principles for the extremal eigenvalues of the Ginibre ensembles with good rate functions. In contrast to the typical estimates for the extremal eigenvalues, the large deviations for the real Ginibre ensemble come from the eigenvalues lying on the real line. Moreover, we also derive deviation estimates for the second leading term in the asymptotic expansion of the extremal eigenvalues. These polynomially small deviation estimates are universal for any i.i.d. matrices under a mild moment condition.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1555 - 1571"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261960","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
A Moment Bound on Bulk/Boundary Quotients of Gaussian Multiplicative Cascades 高斯乘级联的体积/边界商的矩界
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-5036-6
Yichao Huang, Youtao Liu
{"title":"A Moment Bound on Bulk/Boundary Quotients of Gaussian Multiplicative Cascades","authors":"Yichao Huang,&nbsp;Youtao Liu","doi":"10.1007/s10114-026-5036-6","DOIUrl":"10.1007/s10114-026-5036-6","url":null,"abstract":"<div><p>We initiate the study of bulk/boundary quotients of Gaussian multiplicative cascades measures, for which we establish preliminary joint moment bounds. This is a preliminary result towards studying the bulk/boundary quotients of Gaussian multiplicative chaos measures coming from the theory of boundary Liouville conformal field theory.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1713 - 1726"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261961","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
Increasing Paths on N-ary Trees 在n树上增加路径
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-5033-9
Xinxin Chen
{"title":"Increasing Paths on N-ary Trees","authors":"Xinxin Chen","doi":"10.1007/s10114-026-5033-9","DOIUrl":"10.1007/s10114-026-5033-9","url":null,"abstract":"<div><p>Consider a rooted <i>N</i>-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible vertices and kill all the others. For any positive constant <i>α</i>, we describe the asymptotic behaviors of the population at the <i>αN</i>-th generation as <i>N</i> goes to infinity. We also study the criticality of the survival probability at the <span>((eN-frac{3}{2}{rm{log}}N))</span>-th generation in this paper.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1685 - 1712"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261760","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 for the Maximum of a Reducible Two-type Branching Brownian Motion 可约两型分支布朗运动最大值的大偏差
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4393-5
Hui He
{"title":"Large Deviations for the Maximum of a Reducible Two-type Branching Brownian Motion","authors":"Hui He","doi":"10.1007/s10114-026-4393-5","DOIUrl":"10.1007/s10114-026-4393-5","url":null,"abstract":"<div><p>We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motions and create offspring at a constant rate. Particles of type 1 can give birth to particles of types 1 and 2, but particles of type 2 only give birth to descendants of type 2. Under some specific conditions, Belloum and Mallein showed that the maximum position <i>M</i><sub><i>t</i></sub> of all particles alive at time <i>t</i>, suitably centered by a deterministic function <i>m</i><sub><i>t</i></sub>, converge weakly. In this work, we are interested in the decay rate of the following upper large deviation probability, as <i>t</i> → ∞</p><div><div><span>$$mathbb{P}(M_{t}geq theta m_{t}), quad theta &gt;1.$$</span></div></div><p>We shall show that the decay rate function exhibits phase transitions depending on certain relations between <i>θ</i>, the variance of the underlying Brownian motion and the branching rate.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1621 - 1638"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261963","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
A Central Limit Theorem for Square Ice 方形冰的中心极限定理
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4385-5
Wei Wu
{"title":"A Central Limit Theorem for Square Ice","authors":"Wei Wu","doi":"10.1007/s10114-026-4385-5","DOIUrl":"10.1007/s10114-026-4385-5","url":null,"abstract":"<div><p>We prove that the height function associated with the uniform six-vertex model (or equivalently, the uniform homomorphism height function from ℤ<sup>2</sup> to ℤ) satisfies a central limit theorem, upon some logarithmic rescaling.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1609 - 1620"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261965","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
Joint Scaling Limit of a Bipolar-Oriented Triangulation and Its Dual in the Peanosphere Sense 双极定向三角剖分的联合标度极限及其对偶
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-06-15 DOI: 10.1007/s10114-026-4359-7
Ewain Gwynne, Nina Holden, Xin Sun
{"title":"Joint Scaling Limit of a Bipolar-Oriented Triangulation and Its Dual in the Peanosphere Sense","authors":"Ewain Gwynne,&nbsp;Nina Holden,&nbsp;Xin Sun","doi":"10.1007/s10114-026-4359-7","DOIUrl":"10.1007/s10114-026-4359-7","url":null,"abstract":"<div><p>Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this encoding together with the mating-of-trees construction of Liouville quantum gravity (LQG) due to Duplantier, Miller, and Sheffield (2014), they proved that random bipolar-oriented planar maps converge in the scaling limit to a <span>(sqrt{4over{3}})</span>-LQG surface decorated by an independent SLE<sub>12</sub> in the peanosphere sense, meaning that the height functions of a particular pair of trees on the maps converge in the scaling limit to the correlated planar Brownian motion which encodes the SLE-decorated LQG surface. We improve this convergence result by proving that the pair of height functions for an infinite-volume random bipolar-oriented triangulation and the pair of height functions for its dual map converge jointly in law in the scaling limit to the two planar Brownian motions which encode the same <span>(sqrt{4over{3}})</span>-LQG surface decorated by both an SLE<sub>12</sub> curve and the “dual” SLE<sub>12</sub> curve which travels in a direction perpendicular (in the sense of imaginary geometry) to the original curve. This confirms a conjecture of Kenyon, Miller, Sheffield, and Wilson (2015). Our paper is the starting point of recent works connecting LQG and random permutons such as the Baxter permuton.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1509 - 1554"},"PeriodicalIF":0.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261761","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
Very Ampleness Part of Fujita Conjecture and Multiplier Ideal Sheaves of Higher Order 藤田猜想的极大丰度部分及高阶乘法器理想束
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-05-15 DOI: 10.1007/s10114-026-6229-8
Yum-Tong Siu
{"title":"Very Ampleness Part of Fujita Conjecture and Multiplier Ideal Sheaves of Higher Order","authors":"Yum-Tong Siu","doi":"10.1007/s10114-026-6229-8","DOIUrl":"10.1007/s10114-026-6229-8","url":null,"abstract":"<div><p>There are two parts in the Fujita conjecture of 1987. One is the freeness part which since 1995 has been proved with various weaker bounds. The other is the very ampleness part, which remains open even with weaker bounds. Here we will present a proof of the very ampleness part of the Fujita conjecture with a weaker bound by the method of multiplier ideal sheaves of higher order. Moreover, we prove the following more general main result. For an ample line bundle <i>L</i> on a compact complex manifold <i>X</i> of complex dimension <i>n</i>, any prescribed (<i>q</i><sub><i>j</i></sub> − 1)-jets at prescribed points <i>P</i><sub><i>j</i></sub> of <i>X</i> for 1 ≤ <i>j</i> ≤ <i>k</i> can be achieved by a global holomorphic section of <i>mL</i> + <i>K</i><sub><i>X</i></sub> for <i>m</i> ≥ <i>m</i><sub>0</sub> with <i>m</i><sub>0</sub> explicitly computable from <i>n,q</i><sub>1</sub>,…,<i>q</i><sub><i>k</i></sub>. This article is a write-up of my talk given on April 21, 2024 in the Conference on Several Complex Variables and Complex Geometry at Beijing Normal University. This write-up keeps the conversational style of my talk.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1149 - 1157"},"PeriodicalIF":0.9,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173240","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
Infinite Differentiability of the Free Energy for a Derrida–Retaux System Derrida-Retaux系统自由能的无穷可微性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-05-07 DOI: 10.1007/s10114-026-4249-z
Xinxing Chen
{"title":"Infinite Differentiability of the Free Energy for a Derrida–Retaux System","authors":"Xinxing Chen","doi":"10.1007/s10114-026-4249-z","DOIUrl":"10.1007/s10114-026-4249-z","url":null,"abstract":"<div><p>We consider a recursive system which was introduced by Derrida and Retaux (<i>J. Stat. Phys.</i>, <b>156</b>, 268–290 (2014)) as a toy model to study the depinning transition in presence of disorder. Derrida and Retaux predicted the free energy <i>F</i><sub>∞</sub>(<i>p</i>) of the system exhibit quite an unusual physical phenomenon which is an infinite order phase transition. Hu and Shi (<i>J. Stat. Phys.</i>, <b>172</b>, 718–741 (2018)) studied a special situation and obtained other behavior of the free energy, while insisted on <i>p</i> = <i>p</i><sub><i>c</i></sub> being an essential singularity. Recently, Chen, Dagard, Derrida, Hu, Lifshits and Shi (<i>Ann. Probab.</i>, <b>49</b>, 637–670 (2021)) confirmed the Derrida–Retaux conjecture under suitable integrability condition. However, from a mathematical point of view, it is still unknown whether the free energy is infinitely differentiable at the critical point. So we continue to study the infinite differentiability of the free energy in this paper.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 on","pages":"1457 - 1480"},"PeriodicalIF":0.9,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261843","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
Analytic Properties of Speyer’s g-polynomial of Uniform Matroids 一致拟阵的Speyer g-多项式的解析性质
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4502-5
Rong Zhang, James J. Y. Zhao
{"title":"Analytic Properties of Speyer’s g-polynomial of Uniform Matroids","authors":"Rong Zhang,&nbsp;James J. Y. Zhao","doi":"10.1007/s10114-026-4502-5","DOIUrl":"10.1007/s10114-026-4502-5","url":null,"abstract":"<div><p>Let <i>U</i><sub><i>n,d</i></sub> denote the uniform matroid of rank <i>d</i> on <i>n</i> elements. We obtain some recurrence relations satisfied by Speyer’s <i>g</i>-polynomials <i>g</i><i><span>u</span></i><sub><i>n,d</i></sub>(<i>t</i>) of <i>U</i><sub><i>n,d</i></sub>. Based on these recurrence relations, we prove that the polynomial <i>g</i><i><span>u</span></i><sub><i>n,d</i></sub>(<i>t</i>) has only real zeros for any <i>n</i> − 1 ≥ <i>d</i> ≥ 1. Furthermore, we show that the coefficient of <i>g</i><i><span>u</span></i><sub><i>n</i>,[<i>n</i>/2]</sub>(<i>t</i>) is asymptotically normal by local and central limit theorems.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1087 - 1098"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827027","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书