Inventiones mathematicae最新文献_第3页

On ends of finite-volume noncompact manifolds of nonpositive curvature 论非正曲率有限体积非紧凑流形的末端

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00222-024-01266-0

Ran Ji, Yunhui Wu

引用次数: 0

Percolation transition for random forests in $dgeqslant 3$ 随机森林在$dgeqslant 3$中的渗透过渡

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-15 DOI: 10.1007/s00222-024-01263-3

Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth

{"title":"Percolation transition for random forests in $dgeqslant 3$","authors":"Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth","doi":"10.1007/s00222-024-01263-3","DOIUrl":"https://doi.org/10.1007/s00222-024-01263-3","url":null,"abstract":"The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor (beta >0) per edge. It arises as the (qto 0) limit of the (q)-state random cluster model with (p=beta q). We prove that in dimensions (dgeqslant 3) the arboreal gas undergoes a percolation phase transition. This contrasts with the case of (d=2) where no percolation transition occurs.The starting point for our analysis is an exact relationship between the arboreal gas and a non-linear sigma model with target space the fermionic hyperbolic plane (mathbb{H}^{0|2}). This latter model can be thought of as the 0-state Potts model, with the arboreal gas being its random cluster representation. Unlike the standard Potts models, the (mathbb{H}^{0|2}) model has continuous symmetries. By combining a renormalisation group analysis with Ward identities we prove that this symmetry is spontaneously broken at low temperatures. In terms of the arboreal gas, this symmetry breaking translates into the existence of infinite trees in the thermodynamic limit. Our analysis also establishes massless free field correlations at low temperatures and the existence of a macroscopic tree on finite tori.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"187 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059461","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

Strong asymptotic freeness for independent uniform variables on compact groups associated to nontrivial representations 与非微观表征相关的紧凑群上独立均匀变量的强渐近自由性

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-07 DOI: 10.1007/s00222-024-01259-z

Charles Bordenave, Benoît Collins

{"title":"Strong asymptotic freeness for independent uniform variables on compact groups associated to nontrivial representations","authors":"Charles Bordenave, Benoît Collins","doi":"10.1007/s00222-024-01259-z","DOIUrl":"https://doi.org/10.1007/s00222-024-01259-z","url":null,"abstract":"Voiculescu discovered asymptotic freeness of independent Haar-distributed unitary matrices. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random permutations acting on the orthogonal of the Perron-Frobenius eigenvector. In this paper, we consider a new matrix unitary model appearing naturally from representation theory of compact groups. We fix a nontrivial signature (rho ), i.e. two finite sequences of non-increasing natural numbers, and for (n) large enough, consider the irreducible representation (V_{n,rho }) of (mathbb{U}_{n}) associated with the signature (rho ). We consider the quotient (mathbb{U}_{n,rho }) of (mathbb{U}_{n}) viewed as a matrix subgroup of (mathbb{U}(V_{n,rho })), and show that strong asymptotic freeness holds in this generalized context when drawing independent copies of the Haar measure. We also obtain the orthogonal variant of this result. Thanks to classical results in representation theory, this result is closely related to strong asymptotic freeness for tensors, which we establish as a preliminary. To achieve this result, we need to develop four new tools, each of independent theoretical interest: (i) a centered Weingarten calculus and uniform estimates thereof, (ii) a systematic and uniform comparison of Gaussian moments and unitary moments of matrices, (iii) a generalized and simplified operator-valued non-backtracking theory in a general (C^{*})-algebra, and finally, (iv) combinatorics of tensor moment matrices.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"56 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934763","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 cubulation of strict hyperbolization 严格双曲面的特殊立方体

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-02 DOI: 10.1007/s00222-024-01241-9

Jean-François Lafont, Lorenzo Ruffoni

引用次数: 0

Vanishing viscosity limit for axisymmetric vortex rings 轴对称涡环的消失粘度极限

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-29 DOI: 10.1007/s00222-024-01261-5

Thierry Gallay, Vladimír Šverák

{"title":"Vanishing viscosity limit for axisymmetric vortex rings","authors":"Thierry Gallay, Vladimír Šverák","doi":"10.1007/s00222-024-01261-5","DOIUrl":"https://doi.org/10.1007/s00222-024-01261-5","url":null,"abstract":"For the incompressible Navier-Stokes equations in (mathbb{R}^{3}) with low viscosity (nu >0), we consider the Cauchy problem with initial vorticity (omega _{0}) that represents an infinitely thin vortex filament of arbitrary given strength (Gamma ) supported on a circle. The vorticity field (omega (x,t)) of the solution is smooth at any positive time and corresponds to a vortex ring of thickness (sqrt{nu t}) that is translated along its symmetry axis due to self-induction, an effect anticipated by Helmholtz in 1858 and quantified by Kelvin in 1867. For small viscosities, we show that (omega (x,t)) is well-approximated on a large time interval by (omega _{mathrm {lin}}(x-a(t),t)), where (omega _{mathrm {lin}}(cdot ,t)=exp (nu tDelta )omega _{0}) is the solution of the heat equation with initial data (omega _{0}), and (dot{a}(t)) is the instantaneous velocity given by Kelvin’s formula. This gives a rigorous justification of the binormal motion for circular vortex filaments in weakly viscous fluids. The proof relies on the construction of a precise approximate solution, using a perturbative expansion in self-similar variables. To verify the stability of this approximation, one needs to rule out potential instabilities coming from very large advection terms in the linearized operator. This is done by adapting V. I. Arnold’s geometric stability methods developed in the inviscid case (nu =0) to the slightly viscous situation. It turns out that although the geometric structures behind Arnold’s approach are no longer preserved by the equation for (nu > 0), the relevant quadratic forms behave well on larger subspaces than those originally used in Arnold’s theory and interact favorably with the viscous terms.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"36 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811860","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

Finite quotients of 3-manifold groups 3 个网格群的有限商

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-29 DOI: 10.1007/s00222-024-01262-4

Will Sawin, Melanie Matchett Wood

引用次数: 0

Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation 三维立方非线性波方程的吉布斯不变度量

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-29 DOI: 10.1007/s00222-024-01254-4

Bjoern Bringmann, Yu Deng, Andrea R. Nahmod, Haitian Yue

{"title":"Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation","authors":"Bjoern Bringmann, Yu Deng, Andrea R. Nahmod, Haitian Yue","doi":"10.1007/s00222-024-01254-4","DOIUrl":"https://doi.org/10.1007/s00222-024-01254-4","url":null,"abstract":"We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic (Phi ^{4}_{3})-model. This result is the hyperbolic counterpart to seminal works on the parabolic (Phi ^{4}_{3})-model by Hairer (Invent. Math. 198(2):269–504, 2014) and Hairer-Matetski (Ann. Probab. 46(3):1651–1709, 2018).The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates.The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"22 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812105","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

Mean curvature flow with generic initial data 具有一般初始数据的平均曲率流

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-23 DOI: 10.1007/s00222-024-01258-0

Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze

引用次数: 0

Persistence of heterodimensional cycles 异维周期的持续性

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s00222-024-01255-3

Dongchen Li, Dmitry Turaev

引用次数: 0

A predicted distribution for Galois groups of maximal unramified extensions 最大非ramified扩展的伽罗瓦群的预测分布

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s00222-024-01257-1

Yuan Liu, Melanie Matchett Wood, David Zureick-Brown

{"title":"A predicted distribution for Galois groups of maximal unramified extensions","authors":"Yuan Liu, Melanie Matchett Wood, David Zureick-Brown","doi":"10.1007/s00222-024-01257-1","DOIUrl":"https://doi.org/10.1007/s00222-024-01257-1","url":null,"abstract":"We consider the distribution of the Galois groups (operatorname {Gal}(K^{operatorname{un}}/K)) of maximal unramified extensions as (K) ranges over (Gamma )-extensions of ℚ or ({{mathbb{F}}}_{q}(t)). We prove two properties of (operatorname {Gal}(K^{operatorname{un}}/K)) coming from number theory, which we use as motivation to build a probability distribution on profinite groups with these properties. In Part I, we build such a distribution as a limit of distributions on (n)-generated profinite groups. In Part II, we prove as (qrightarrow infty ), agreement of (operatorname {Gal}(K^{operatorname{un}}/K)) as (K) varies over totally real (Gamma )-extensions of ({{mathbb{F}}}_{q}(t)) with our distribution from Part I, in the moments that are relatively prime to (q(q-1)|Gamma |). In particular, we prove for every finite group (Gamma ), in the (qrightarrow infty ) limit, the prime-to-(q(q-1)|Gamma |)-moments of the distribution of class groups of totally real (Gamma )-extensions of ({{mathbb{F}}}_{q}(t)) agree with the prediction of the Cohen–Lenstra–Martinet heuristics.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"38 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572872","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