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Communications on Pure and Applied Mathematics最新文献

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Boundary statistics for the six‐vertex model with DWBC
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
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
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
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
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
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
Analysis of density matrix embedding theory around the non‐interacting limit
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-02-04 DOI: 10.1002/cpa.22244
Eric Cancès, Fabian M. Faulstich, Alfred Kirsch, Eloïse Letournel, Antoine Levitt
{"title":"Analysis of density matrix embedding theory around the non‐interacting limit","authors":"Eric Cancès, Fabian M. Faulstich, Alfred Kirsch, Eloïse Letournel, Antoine Levitt","doi":"10.1002/cpa.22244","DOIUrl":"https://doi.org/10.1002/cpa.22244","url":null,"abstract":"This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii) DMET is exact up to first order in the coupling parameter. We provide numerical simulations to support our results and comment on the physical meaning of the assumptions under which they hold true. We show that the violation of these assumptions may yield multiple solutions to the DMET equations. We moreover introduce and discuss a specific ‐representability problem inherent to DMET.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"55 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125219","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
Special Lagrangian pair of pants
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1002/cpa.22248
Yang Li
{"title":"Special Lagrangian pair of pants","authors":"Yang Li","doi":"10.1002/cpa.22248","DOIUrl":"https://doi.org/10.1002/cpa.22248","url":null,"abstract":"We construct special Lagrangian pair of pants in general dimensions, inside the cotangent bundle of with the Euclidean structure, building upon earlier topological ideas of Matessi. The construction uses a combination of PDE and geometric measure theory.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"7 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056314","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
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