发布求助
文献互助 智能选刊 最新文献

Communications on Pure and Applied Mathematics最新文献

筛选
英文 中文
Boundary conditions and universal finite‐size scaling for the hierarchical |φ|4$|varphi |^4$ model in dimensions 4 and higher 4维及以上层次|φ|4$|varphi |^4$模型的边界条件和通用有限尺寸标度
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-29 DOI: 10.1002/cpa.22256
Emmanuel Michta, Jiwoon Park, Gordon Slade
{"title":"Boundary conditions and universal finite‐size scaling for the hierarchical |φ|4$|varphi |^4$ model in dimensions 4 and higher","authors":"Emmanuel Michta, Jiwoon Park, Gordon Slade","doi":"10.1002/cpa.22256","DOIUrl":"https://doi.org/10.1002/cpa.22256","url":null,"abstract":"We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical ‐component model for all integers in all dimensions , for both free and periodic boundary conditions. For , we prove that for a volume of size with periodic boundary conditions the infinite‐volume critical point is an effective finite‐volume critical point, whereas for free boundary conditions the effective critical point is shifted smaller by an amount of order . For both boundary conditions, the average field has the same non‐Gaussian limit within a critical window of width around the effective critical point, and in that window we compute the universal scaling profile for the susceptibility. In contrast, and again for both boundary conditions, the average field has a massive Gaussian limit when above the effective critical point by an amount . In particular, at the infinite‐volume critical point the susceptibility scales as for periodic boundary conditions and as for free boundary conditions. We identify a mass generation mechanism for free boundary conditions that is responsible for this distinction and which we believe has wider validity, in particular to Euclidean (non‐hierarchical) models on in dimensions . For we prove a similar picture with logarithmic corrections. Our analysis is based on the rigorous renormalisation group method of Bauerschmidt, Brydges and Slade, which we improve and extend.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"88 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889831","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
Persistence and ball exponents for Gaussian stationary processes 高斯平稳过程的持续性和球指数
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-29 DOI: 10.1002/cpa.22255
Naomi D. Feldheim, Ohad N. Feldheim, Sumit Mukherjee
{"title":"Persistence and ball exponents for Gaussian stationary processes","authors":"Naomi D. Feldheim, Ohad N. Feldheim, Sumit Mukherjee","doi":"10.1002/cpa.22255","DOIUrl":"https://doi.org/10.1002/cpa.22255","url":null,"abstract":"Consider a real Gaussian stationary process , indexed on either or and admitting a spectral measure . We study , the persistence exponent of . We show that, if has a positive density at the origin, then the persistence exponent exists; moreover, if has an absolutely continuous component, then if and only if this spectral density at the origin is finite. We further establish continuity of in , in (under a suitable metric) and, if is compactly supported, also in dense sampling. Analogous continuity properties are shown for , the ball exponent of , and it is shown to be positive if and only if has an absolutely continuous component.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"222 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889830","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
Boundary statistics for the six‐vertex model with DWBC 带有DWBC的六顶点模型的边界统计
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-24 DOI: 10.1002/cpa.22254
Vadim Gorin, Karl Liechty
{"title":"Boundary statistics for the six‐vertex model with DWBC","authors":"Vadim Gorin, Karl Liechty","doi":"10.1002/cpa.22254","DOIUrl":"https://doi.org/10.1002/cpa.22254","url":null,"abstract":"We study the behavior of configurations in the symmetric six‐vertex model with weights in the square with Domain Wall Boundary Conditions as . We prove that when , configurations near the boundary have fluctuations of order and are asymptotically described by the GUE‐corners process of random matrix theory. On the other hand, when , the fluctuations are of finite order and configurations are asymptotically described by the stochastic six‐vertex model in a quadrant. In the special case (which implies ), the limit is expressed as the ‐exchangeable random permutation of infinitely many letters, distributed according to the infinite Mallows measure.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"74 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143872730","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
On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation 能量临界等变调和映射热流和径向非线性热方程的全局动力学分类
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-18 DOI: 10.1002/cpa.22253
Kihyun Kim, Frank Merle
{"title":"On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation","authors":"Kihyun Kim, Frank Merle","doi":"10.1002/cpa.22253","DOIUrl":"https://doi.org/10.1002/cpa.22253","url":null,"abstract":"We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the maximal time of existence. Our main result for (HMHF) gives a complete classification of their dynamics for equivariance indices ; (i) they exist globally in time, (ii) the number of bubbles and signs are determined by the energy class of the initial data, and (iii) the scales of bubbles are asymptotically given by a universal sequence of rates up to scaling symmetry. In parallel, we also obtain a complete classification of ‐bounded radial solutions to (NLH) in dimensions , building upon soliton resolution for such solutions. To our knowledge, this provides the first rigorous classification of bubble tree dynamics within symmetry. We introduce a new approach based on the energy method that does not rely on maximum principle. The key ingredient of the proof is a monotonicity estimate near any bubble tree configurations, which in turn requires a delicate construction of modified multi‐bubble profiles also.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847057","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
Maximum of the characteristic polynomial of i.i.d. matrices i.i.d. 矩阵特征多项式的最大值
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-08 DOI: 10.1002/cpa.22250
Giorgio Cipolloni, Benjamin Landon
{"title":"Maximum of the characteristic polynomial of i.i.d. matrices","authors":"Giorgio Cipolloni, Benjamin Landon","doi":"10.1002/cpa.22250","DOIUrl":"https://doi.org/10.1002/cpa.22250","url":null,"abstract":"We compute the leading order asymptotic of the maximum of the characteristic polynomial for i.i.d. matrices with real or complex entries. In particular, this result is new even for real Ginibre matrices, which was left as an open problem in Lambert et al. Electron. J. Probab. 29 (2024); the complex Ginibre case was covered in Lambert, Comm. Math Phys. 378 (2020). These are the first universality results for the non‐Hermitian analog of the first order term of the Fyodorov–Hiary–Keating conjecture. Our methods are based on constructing a coupling to the branching random walk (BRW) via Dyson Brownian motion. In particular, we find a new connection between real i.i.d. matrices and inhomogeneous BRW.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143805899","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
Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature 非负Ricci曲率非紧流形中大等周集的平均唯一性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-05 DOI: 10.1002/cpa.22252
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola
{"title":"Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature","authors":"Gioacchino Antonelli, Marco Pozzetta, Daniele Semola","doi":"10.1002/cpa.22252","DOIUrl":"https://doi.org/10.1002/cpa.22252","url":null,"abstract":"Let be a complete Riemannian manifold which is not isometric to , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set with density 1 at infinity such that for every there is a unique isoperimetric set of volume in ; moreover, its boundary is strictly volume preserving stable. The latter result cannot be improved to uniqueness or strict stability for every large volume. Indeed, we construct a complete Riemannian surface satisfying the previous assumptions and with the following additional property: there exist arbitrarily large and diverging intervals such that isoperimetric sets with volumes exist, but they are neither unique nor do they have strictly volume preserving stable boundaries.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"73 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143782633","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
The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion 多孔介质方程：具有退化和无约束扩散的大偏差和梯度流动
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-04-05 DOI: 10.1002/cpa.22251
Benjamin Gess, Daniel Heydecker
{"title":"The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion","authors":"Benjamin Gess, Daniel Heydecker","doi":"10.1002/cpa.22251","DOIUrl":"https://doi.org/10.1002/cpa.22251","url":null,"abstract":"The problem of deriving a gradient flow structure for the porous medium equation which is <jats:italic>thermodynamic</jats:italic>, in that it arises from the large deviations of some microscopic particle system is studied. To this end, a rescaled zero‐range process with jump rate is considered, and its hydrodynamic limit and dynamical large deviations are shown in the presence of both degenerate and unbounded diffusion. The key super‐exponential estimate is obtained using pathwise discretised regularity estimates in the spirit of the Aubin–Lions–Simons lemma. This allows to exhibit the porous medium equation as the gradient flow of the entropy in a thermodynamic metric via the energy‐dissipation inequality.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143782632","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
First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet 一阶Sobolev空间，自相似能量和Sierpiński地毯上的能量度量
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-02-18 DOI: 10.1002/cpa.22247
Mathav Murugan, Ryosuke Shimizu
{"title":"First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet","authors":"Mathav Murugan, Ryosuke Shimizu","doi":"10.1002/cpa.22247","DOIUrl":"https://doi.org/10.1002/cpa.22247","url":null,"abstract":"For any , we construct ‐energies and the corresponding ‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular conformal dimension is attained on the Sierpiński carpet. If the Ahlfors regular conformal dimension is attained, we show that any optimal Ahlfors regular measure attaining the Ahlfors regular conformal dimension must necessarily be a bounded perturbation of the ‐energy measure of some function in our Sobolev space, where is the Ahlfors regular conformal dimension. Under the attainment of the Ahlfors regular conformal dimension, the ‐Newtonian Sobolev space corresponding to any optimal Ahlfors regular metric and measure is shown to coincide with our Sobolev space with comparable norms, where is the Ahlfors regular conformal dimension.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"12 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443282","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
On the Read‐Shockley energy for grain boundaries in 2D polycrystals 二维多晶晶界的Read - Shockley能
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-02-11 DOI: 10.1002/cpa.22245
Martino Fortuna, Adriana Garroni, Emanuele Spadaro
{"title":"On the Read‐Shockley energy for grain boundaries in 2D polycrystals","authors":"Martino Fortuna, Adriana Garroni, Emanuele Spadaro","doi":"10.1002/cpa.22245","DOIUrl":"https://doi.org/10.1002/cpa.22245","url":null,"abstract":"In the 50's Read and Shockley proposed a formula for the energy of small angle grain boundaries in polycrystals based on linearized elasticity and an ansatz on the distribution of incompatibilities of the lattice at the interface between two grains. The logarithmic scaling of this formula has been rigorously justified without any ansatz on the geometry of dislocations only recently in an article by Lauteri and Luckhaus. In the present paper, building upon their analysis, we derive a two dimensional sharp interface limiting functional starting from the nonlinear semi‐discrete model introduced in Lauteri and Luckhaus: the line tension we obtain via ‐convergence depends on the rotations of the grains and the relative orientations of the interfaces, and for small angle grain boundaries has the Read and Shockley logarithmic scaling.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143384980","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
Stability of perfectly matched layers for Maxwell's equations in rectangular solids 矩形固体中麦克斯韦方程组完美匹配层的稳定性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-02-11 DOI: 10.1002/cpa.22249
Laurence Halpern, Jeffrey Rauch
{"title":"Stability of perfectly matched layers for Maxwell's equations in rectangular solids","authors":"Laurence Halpern, Jeffrey Rauch","doi":"10.1002/cpa.22249","DOIUrl":"https://doi.org/10.1002/cpa.22249","url":null,"abstract":"Perfectly matched layers are extensively used to compute approximate solutions for Maxwell's equations in using a bounded computational domain, usually a rectangular solid. A smaller rectangular domain of interest is surrounded by layers designed to absorb outgoing waves in perfectly reflectionless manner. On the boundary of the computational domain, an absorbing boundary condition is imposed that is necessarily imperfect. The method replaces the Maxwell equations by a larger system, and introduces absorption coefficients positive in the layers. Well posedness of the resulting initial boundary value problem is proved here for the first time. The Laplace transform of a resulting Helmholtz system is studied. For positive real values of the transform variable , the Helmholtz system has a unique solution from a variational form that yields limited regularity for rectangular domains. When is not real the complex variational form loses positivity. We smooth the domain and, in spite of this loss, construct solutions with uniform estimates. Using the regularity, we deduce Maxwell from Helmholtz, then remove the smoothing. The boundary condition at the smoothed boundary must be carefully chosen. A method of Jerison‐Kenig‐Mitrea is extended to compensate the nonpositivity of the flux.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"41 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143393170","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
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：481959085
Book学术官方微信