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A Localized Construction of Kasner-like Singularities 类kasner奇点的局域构造
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05437-9
Nikolaos Athanasiou, Grigorios Fournodavlos
{"title":"A Localized Construction of Kasner-like Singularities","authors":"Nikolaos Athanasiou,&nbsp;Grigorios Fournodavlos","doi":"10.1007/s00220-025-05437-9","DOIUrl":"10.1007/s00220-025-05437-9","url":null,"abstract":"<div><p>We construct local, in spacetime, singular solutions to the Einstein vacuum equations that exhibit Kasner-like behavior in their past boundary. Our result can be viewed as a localization (in space) of the construction in [18]. We also prove a refined uniqueness statement and give a simple argument that generates general asymptotic data for Kasner-like singularities, enjoying all expected degrees of freedom, albeit only locally in space. The key difference of the present work with [18] is our use of a first order symmetric hyperbolic formulation of the Einstein vacuum equations, relative to the connection coefficients of a parallelly propagated orthonormal frame which is adapted to the Gaussian time foliation. This makes it easier to localize the construction, since elliptic estimates are no longer required to complete the energy argument.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simplicity of C*-Algebras of Contracting Self-Similar Groups 缩并自相似群的C*-代数的简单性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05411-5
Eusebio Gardella, Volodymyr Nekrashevych, Benjamin Steinberg, Alina Vdovina
{"title":"Simplicity of C*-Algebras of Contracting Self-Similar Groups","authors":"Eusebio Gardella,&nbsp;Volodymyr Nekrashevych,&nbsp;Benjamin Steinberg,&nbsp;Alina Vdovina","doi":"10.1007/s00220-025-05411-5","DOIUrl":"10.1007/s00220-025-05411-5","url":null,"abstract":"<div><p>We show that the <span>(C^*)</span>-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex <span>(*)</span>-algebra is simple. We also improve on Steinberg and Szakács’s algorithm to determine if the <span>(*)</span>-algebra is simple. This provides an interesting class of non-Hausdorff, amenable, effective and minimal ample groupoids for which simplicity of the <span>(C^*)</span>-algebra and the complex <span>(*)</span>-algebra are equivalent.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SDEs with Supercritical Distributional Drifts 具有超临界分布漂移的SDEs
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05430-2
Zimo Hao, Xicheng Zhang
{"title":"SDEs with Supercritical Distributional Drifts","authors":"Zimo Hao,&nbsp;Xicheng Zhang","doi":"10.1007/s00220-025-05430-2","DOIUrl":"10.1007/s00220-025-05430-2","url":null,"abstract":"<div><p>Let <span>(dgeqslant 2)</span>. In this paper, we investigate the following stochastic differential equation (SDE) in <span>({{mathbb {R}}}^d)</span> driven by Brownian motion </p><div><div><span>$$ textrm{d} X_t=b(t,X_t)textrm{d} t+sqrt{2}textrm{d} W_t, $$</span></div></div><p>where <i>b</i> belongs to the space <span>({{mathbb {L}}}_T^q textbf{H}_p^alpha )</span> with <span>(alpha in [-1, 0])</span> and <span>(p,qin [2, infty ])</span>, which is a distribution-valued and divergence-free vector field. In the subcritical case <span>(frac{d}{p}+frac{2}{q}&lt;1+alpha )</span>, we establish the existence and uniqueness of a weak solution to the integral equation: </p><div><div><span>$$ X_t=X_0+lim _{nrightarrow infty }int ^t_0b_n(s,X_s)textrm{d} s+sqrt{2} W_t. $$</span></div></div><p>Here, <span>(b_n:=b*phi _n)</span> represents the mollifying approximation, and the limit is taken in the <span>(L^2)</span>-sense. In the critical and supercritical case <span>(1+alpha leqslant frac{d}{p}+frac{2}{q}&lt;2+alpha )</span>, assuming the initial distribution has an <span>(L^2)</span>-density, we show the existence of weak solutions and associated Markov processes. Moreover, under the additional assumption that <span>(b=b_1+b_2+mathord {textrm{div}}a)</span>, where <span>(b_1in {{mathbb {L}}}^infty _T{{textbf{B}}}^{-1}_{infty ,2})</span>, <span>(b_2in {{mathbb {L}}}^2_TL^2)</span>, and <i>a</i> is a bounded antisymmetric matrix-valued function, we establish the convergence of mollifying approximation solutions without the need to subtract a subsequence. To illustrate our results, we provide examples of Gaussian random fields and singular interacting particle systems, including the two-dimensional vortex models.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(C^*)-Framework for Higher-Order Bulk-Boundary Correspondences (C^*)-高阶本体边界对应的框架
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05415-1
Danilo Polo Ojito, Emil Prodan, Tom Stoiber
{"title":"(C^*)-Framework for Higher-Order Bulk-Boundary Correspondences","authors":"Danilo Polo Ojito,&nbsp;Emil Prodan,&nbsp;Tom Stoiber","doi":"10.1007/s00220-025-05415-1","DOIUrl":"10.1007/s00220-025-05415-1","url":null,"abstract":"<div><p>A typical crystal is a finite piece of a material which may be invariant under some point symmetry group. If it is a so-called <i>intrinsic</i> higher-order topological insulator or superconductor, then it displays boundary modes at hinges or corners protected by the crystalline symmetry and the bulk topology. We explain the mechanism behind such phenomena using operator K-theory. Specifically, we derive a groupoid <span>(C^*)</span>-algebra that (1) encodes the dynamics of the electrons in the infinite size limit of a crystal; (2) remembers the boundary conditions at the crystal’s boundaries, and (3) admits a natural action by the point symmetries of the atomic lattice. The filtrations of the groupoid’s unit space by closed subsets that are invariant under the groupoid and point group actions supply equivariant cofiltrations of the groupoid <span>(C^*)</span>-algebra. We show that specific derivations of the induced spectral sequences in twisted equivariant K-theories enumerate all non-trivial higher-order bulk-boundary correspondences.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Log-Hölder Regularity of Stationary Measures Log-Hölder固定措施的规律性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05425-z
Grigorii Monakov
{"title":"Log-Hölder Regularity of Stationary Measures","authors":"Grigorii Monakov","doi":"10.1007/s00220-025-05425-z","DOIUrl":"10.1007/s00220-025-05425-z","url":null,"abstract":"<div><p>We consider Lipschitz and Hölder continuous random dynamical systems defined by a distribution with a finite logarithmic moment. We prove that under suitable non-degeneracy conditions every stationary measure must be <span>(log )</span>-Hölder continuous.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05425-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semilinear Wave Equations on Extremal Reissner–Nordström Black Holes Revisited 极值黑洞Reissner-Nordström的半线性波动方程
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05420-4
Yannis Angelopoulos, Ryan Unger
{"title":"Semilinear Wave Equations on Extremal Reissner–Nordström Black Holes Revisited","authors":"Yannis Angelopoulos,&nbsp;Ryan Unger","doi":"10.1007/s00220-025-05420-4","DOIUrl":"10.1007/s00220-025-05420-4","url":null,"abstract":"<div><p>We revisit global existence and decay for small-data solutions of semilinear wave equations on extremal Reissner–Nordström black hole backgrounds satisfying the classical null condition, a problem which was previously addressed by the first author in joint work with Angelopoulos et al. (Ann PDE 6(2):12, 2020). In this paper, we develop a new approach based on propagating a significantly weaker set of estimates, which allows for a simpler and more streamlined proof. Our proof does not require tracking sharp estimates for the solution in the near-horizon region, which means that it is compatible with, but does not imply, the non-decay and growth hierarchy of derivatives of the solution along the event horizon expected from the Aretakis instability. In particular, this approach is in principle compatible with other settings where stronger horizon instabilities are expected, such as nonlinear charged scalar fields on extremal Reissner–Nordström, or nonlinear waves on extremal Kerr. We also sketch how our proof applies to semilinear problems on spacetimes settling down to extremal Reissner–Nordström, such as those constructed in our joint work with Angelopoulos et al. (Nonlinear stability of extremal Reissner–Nordström black holes in spherical symmetry, 2024. arXiv:2410.16234).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05420-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Wave Equations with Constraints: Well-Posedness and Smoluchowski–Kramers Diffusion Approximation 具有约束的随机波动方程：适定性和Smoluchowski-Kramers扩散近似
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-06 DOI: 10.1007/s00220-025-05397-0
Zdzisław Brzeźniak, Sandra Cerrai
{"title":"Stochastic Wave Equations with Constraints: Well-Posedness and Smoluchowski–Kramers Diffusion Approximation","authors":"Zdzisław Brzeźniak,&nbsp;Sandra Cerrai","doi":"10.1007/s00220-025-05397-0","DOIUrl":"10.1007/s00220-025-05397-0","url":null,"abstract":"<div><p>We investigate the well-posedness of a class of stochastic second-order in time damped evolution equations in Hilbert spaces, subject to the constraint that the solution lies within the unitary sphere. Then, we focus on a specific example, the stochastic damped wave equation in a bounded domain of a <i>d</i>-dimensional Euclidean space, endowed with the Dirichlet boundary condition, with the added constraint that the <span>(L^2)</span>-norm of the solution is equal to one. We introduce a small mass <span>(mu &gt;0)</span> in front of the second-order derivative in time and examine the validity of a Smoluchowski–Kramers diffusion approximation. We demonstrate that, in the small mass limit, the solution converges to the solution of a stochastic parabolic equation subject to the same constraint. We further show that an extra noise-induced drift emerges, which in fact does not account for the Stratonovich-to-Itô correction term.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05397-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Absolute Continuity of the Integrated Density of States in the Localized Regime 局域状态积分密度的绝对连续性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-06 DOI: 10.1007/s00220-025-05406-2
Jing Wang, Xu Xu, Jiangong You, Qi Zhou
{"title":"Absolute Continuity of the Integrated Density of States in the Localized Regime","authors":"Jing Wang,&nbsp;Xu Xu,&nbsp;Jiangong You,&nbsp;Qi Zhou","doi":"10.1007/s00220-025-05406-2","DOIUrl":"10.1007/s00220-025-05406-2","url":null,"abstract":"<div><p>We establish the absolute continuity of the integrated density of states (IDS) for quasi-periodic Schrödinger operators with large trigonometric potentials and Diophantine frequencies. This partially solves Eliasson’s open problem in 2002. Furthermore, this result can be extended to a class of quasi-periodic long-range operators on <span>(ell ^2(mathbb {Z}^d))</span>. Our proof is based on stratified quantitative almost reducibility results of dual cocycles. Specifically, we prove that a generic analytic one-parameter family of cocycles, sufficiently close to constant coefficients, is reducible except for a zero Hausdorff dimension set of parameters. This result affirms Eliasson’s conjecture in 2017.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Marginal Stability in Low Temperature Spherical Spin Glasses 低温球形自旋玻璃的边缘稳定性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-06 DOI: 10.1007/s00220-025-05410-6
Mark Sellke
{"title":"On Marginal Stability in Low Temperature Spherical Spin Glasses","authors":"Mark Sellke","doi":"10.1007/s00220-025-05410-6","DOIUrl":"10.1007/s00220-025-05410-6","url":null,"abstract":"<div><p>We show marginal stability of near-ground states in spherical spin glasses is equivalent to full replica symmetry breaking at zero temperature near overlap 1. This connection has long been implicit in the physics literature, which also links marginal stability to the performance of efficient algorithms. For even models, we prove the Hessian has no outlier eigenvalues, and obtain geometric consequences for low temperature Gibbs measures in the case that marginal stability is absent. Our proofs rely on interpolation bounds for vector spin glass models. For generic models, we give another more conceptual argument that full RSB near overlap 1 implies marginal stability at low temperature.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fusion Products of Twisted Modules in Permutation Orbifolds: II 排列轨道中扭曲模的融合积2
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-08-06 DOI: 10.1007/s00220-025-05404-4
Chongying Dong, Feng Xu, Nina Yu
{"title":"Fusion Products of Twisted Modules in Permutation Orbifolds: II","authors":"Chongying Dong,&nbsp;Feng Xu,&nbsp;Nina Yu","doi":"10.1007/s00220-025-05404-4","DOIUrl":"10.1007/s00220-025-05404-4","url":null,"abstract":"<div><p>Let <i>V</i> be a simple, rational, <span>(C_{2})</span>-cofinite vertex operator algebra of CFT type, and let <i>k</i> be a positive integer. In this paper, we determine the fusion products of twisted modules for <span>(V^{otimes k})</span> and <span>(G = leftlangle g rightrangle )</span> generated by any permutation <span>(g in S_{k})</span>.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","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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