Advances in Mathematics最新文献_第9页

Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices 超临界稀疏维格纳矩阵经验谱测度的大偏差

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-24 DOI: 10.1016/j.aim.2025.110156

Fanny Augeri

{"title":"Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices","authors":"Fanny Augeri","doi":"10.1016/j.aim.2025.110156","DOIUrl":"10.1016/j.aim.2025.110156","url":null,"abstract":"<div><div>Let Ξ be the adjacency matrix of an Erdős-Rényi graph on <em>n</em> vertices and with parameter <em>p</em> and consider <em>A</em> a <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> centred random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree <em>np</em> diverges, the empirical spectral measure of the normalized Hadamard product <span><math><mo>(</mo><mi>A</mi><mo>∘</mo><mi>Ξ</mi><mo>)</mo><mo>/</mo><msqrt><mrow><mi>n</mi><mi>p</mi></mrow></msqrt></math></span> converges weakly in probability to the semicircle law. In the regime where <span><math><mi>p</mi><mo>≪</mo><mn>1</mn></math></span> and <span><math><mi>n</mi><mi>p</mi><mo>≫</mo><mi>log</mi><mo>⁡</mo><mi>n</mi></math></span>, we prove a large deviations principle for the empirical spectral measure with speed <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math></span> and with a good rate function solution of a certain variational problem. The rate function reveals in particular that the only possible deviations at the exponential scale <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math></span> are around measures coming from Quadratic Vector Equations. As a byproduct, we obtain a large deviations principle for the empirical spectral measure of supercritical Erdős-Rényi graphs.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110156"},"PeriodicalIF":1.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143473995","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

Ortho-integral surfaces Ortho-integral表面

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-20 DOI: 10.1016/j.aim.2025.110162

Nhat Minh Doan

引用次数: 0

Norm upper-semicontinuity of functions supported on open abelian isotropy in étale groupoids. Corrigendum to “Reconstruction of groupoids and C⁎-rigidity of dynamical systems” [Adv. Math. 390 (2021) 107923] 在开阿贝尔各向同性上支持的函数的模上半连续性。“群形的重建和动力系统的C - C -刚性”的勘误[Adv. Math. 390 (2021) 107923]

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-20 DOI: 10.1016/j.aim.2025.110150

Toke Meier Carlsen , Anna Duwenig , Efren Ruiz , Aidan Sims

引用次数: 0

On Jacobi–Weierstrass mock modular forms 关于Jacobi-Weierstrass模拟模形式

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.aim.2025.110147

Claudia Alfes , Jens Funke , Michael H. Mertens , Eugenia Rosu

引用次数: 0

The length spectrum of random hyperbolic 3-manifolds 随机双曲型3流形的长度谱

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.aim.2025.110158

Anna Roig-Sanchis

引用次数: 0

The constant term algebra of type A: The structure A型常项代数：结构

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110154

Guoce Xin , Chen Zhang , Yue Zhou , Yueming Zhong

引用次数: 0

An adjunction inequality for the Bauer–Furuta type invariants, with applications to sliceness and 4-manifold topology Bauer-Furuta型不变量的一个附加不等式，及其在切片性和4流形拓扑中的应用

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110134

Nobuo Iida , Anubhav Mukherjee , Masaki Taniguchi

{"title":"An adjunction inequality for the Bauer–Furuta type invariants, with applications to sliceness and 4-manifold topology","authors":"Nobuo Iida , Anubhav Mukherjee , Masaki Taniguchi","doi":"10.1016/j.aim.2025.110134","DOIUrl":"10.1016/j.aim.2025.110134","url":null,"abstract":"<div><div>Our main result gives an adjunction inequality for embedded surfaces in certain 4-manifolds with contact boundary under a non-vanishing assumption on the Bauer–Furuta type invariants. Using this, we give infinitely many knots in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> that are not smoothly H-slice (that is, bounding a null-homologous disk) in many 4-manifolds but they are topologically H-slice. In particular, we give such knots in the boundaries of the punctured elliptic surfaces <span><math><mi>E</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></math></span>. In addition, we give obstructions to codimension-0 orientation-reversing embedding of weak symplectic fillings with <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> into closed symplectic 4-manifolds with <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> and <span><math><msubsup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>≡</mo><mn>3</mn><mi>mod</mi><mspace></mspace><mn>4</mn></math></span>. From here we prove a Bennequin type inequality for strong symplectic caps of <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>d</mi></mrow></msub><mo>)</mo></math></span>. We also show that any weakly symplectically fillable 3-manifold bounds a 4-manifold with at least two smooth structures.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110134"},"PeriodicalIF":1.5,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429200","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

Ergodic measures of intermediate entropies for dynamical systems with the approximate product property 具有近似积性质的动力系统中间熵的遍历测度

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110159

Peng Sun

引用次数: 0

An extended Hilbert scale and its applications 扩展的希尔伯特标度及其应用

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110155

Vladimir Mikhailets , Aleksandr Murach , Tetiana Zinchenko

引用次数: 0

A non-mixing Arnold flow on a surface 表面上的非混合阿诺德流