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Annales Henri Lebesgue最新文献

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The random walk penalised by its range in dimensions d≥3 随机游走在d≥3维的范围内
Annales Henri Lebesgue Pub Date : 2018-11-12 DOI: 10.5802/AHL.66
N. Berestycki, R. Cerf
{"title":"The random walk penalised by its range in dimensions d≥3","authors":"N. Berestycki, R. Cerf","doi":"10.5802/AHL.66","DOIUrl":"https://doi.org/10.5802/AHL.66","url":null,"abstract":"We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close to a solid Euclidean ball of radius approximately $rho_d N^{1/(d+2)}$, for some explicit constant $rho_d >0$. This proves a conjecture of Bolthausen who obtained this result in the case $d=2$.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130240940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Spectral aspects of the Berezin transform Berezin变换的光谱方面
Annales Henri Lebesgue Pub Date : 2018-11-07 DOI: 10.5802/ahl.63
Louis Ioos, V. Kaminker, L. Polterovich, Dor Shmoish
{"title":"Spectral aspects of the Berezin transform","authors":"Louis Ioos, V. Kaminker, L. Polterovich, Dor Shmoish","doi":"10.5802/ahl.63","DOIUrl":"https://doi.org/10.5802/ahl.63","url":null,"abstract":"We discuss the Berezin transform, a Markov operator associated to positive operator valued measures (POVMs), in a number of contexts including the Berezin-Toeplitz quantization, Donaldson's dynamical system on the space of Hermitian products on a complex vector space, representations of finite groups, and quantum noise. In particular, we calculate the spectral gap for quantization in terms of the fundamental tone of the phase space. Our results confirm a prediction of Donaldson for the spectrum of the Q-operator on Kahler manifolds with constant scalar curvature. Furthermore, viewing POVMs as data clouds, we study their spectral features via geometry of measure metric spaces and the diffusion distance.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130581228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Hamilton–Jacobi equations for mean-field disordered systems 平均场无序系统的Hamilton-Jacobi方程
Annales Henri Lebesgue Pub Date : 2018-11-04 DOI: 10.5802/AHL.77
J. Mourrat
{"title":"Hamilton–Jacobi equations for mean-field disordered systems","authors":"J. Mourrat","doi":"10.5802/AHL.77","DOIUrl":"https://doi.org/10.5802/AHL.77","url":null,"abstract":"We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix. We compute the large-scale limit of the free energy by showing that it satisfies an approximate Hamilton-Jacobi equation with asymptotically vanishing viscosity parameter and error term.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122092519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 35
Kesten–McKay law for the Markoff surface mod p Markoff曲面的Kesten-McKay定律
Annales Henri Lebesgue Pub Date : 2018-10-31 DOI: 10.5802/AHL.71
M. D. Courcy-Ireland, Michael Magee
{"title":"Kesten–McKay law for the Markoff surface mod p","authors":"M. D. Courcy-Ireland, Michael Magee","doi":"10.5802/AHL.71","DOIUrl":"https://doi.org/10.5802/AHL.71","url":null,"abstract":"For each prime $p$, we study the eigenvalues of a 3-regular graph on roughly $p^2$ vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKay law, which also describes the eigenvalues of a random regular graph. The proof is based on the method of moments and takes advantage of a natural group action on the Markoff surface.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124218785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Hitting Times and Positions in Rare Events 在罕见事件中击中时间和位置
Annales Henri Lebesgue Pub Date : 2018-10-24 DOI: 10.5802/ahl.154
Roland Zweimüller
{"title":"Hitting Times and Positions in Rare Events","authors":"Roland Zweimüller","doi":"10.5802/ahl.154","DOIUrl":"https://doi.org/10.5802/ahl.154","url":null,"abstract":"We establish abstract limit theorems which provide sufficient conditions for a sequence $(A_{l})$ of rare events in an ergodic probability preserving dynamical system to exhibit Poisson asymptotics, and for the consecutive positions inside the $A_{l}$ to be asymptotically iid (spatiotemporal Poisson limits). The limit theorems only use information on what happens to $A_{l}$ before some time $tau_{l}$ which is of order $o(1/mu(A_{l}))$. In particular, no assumptions on the asymptotic behavior of the system akin to classical mixing conditions are used. We also discuss some general questions about the asymptotic behaviour of spatial and spatiotemporal processes, and illustrate our results in a setup of simple prototypical systems.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129772948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Non-local competition slows down front acceleration during dispersal evolution 在扩散进化过程中，非本地竞争减缓了前沿加速
Annales Henri Lebesgue Pub Date : 2018-10-17 DOI: 10.5802/ahl.117
V. Calvez, Christopher Henderson, S. Mirrahimi, O. Turanova, T. Dumont
{"title":"Non-local competition slows down front acceleration during dispersal evolution","authors":"V. Calvez, Christopher Henderson, S. Mirrahimi, O. Turanova, T. Dumont","doi":"10.5802/ahl.117","DOIUrl":"https://doi.org/10.5802/ahl.117","url":null,"abstract":"We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is non-local with respect to one variable. We prove that the rate of acceleration is slower than the rate of acceleration predicted by the linear problem, that is, without saturation. This hindering phenomenon is the consequence of a subtle interplay between the non-local saturation and the non-trivial dynamics of some particular curves that carry the mass at the front. A careful analysis of these trajectories allows us to identify the value of the rate of acceleration. The article is complemented with numerical simulations that illustrate some behavior of the model that is beyond our analysis.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120955681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Local transversely product singularities 局部横积奇点
Annales Henri Lebesgue Pub Date : 2018-10-09 DOI: 10.5802/AHL.78
A. L. Neto
{"title":"Local transversely product singularities","authors":"A. L. Neto","doi":"10.5802/AHL.78","DOIUrl":"https://doi.org/10.5802/AHL.78","url":null,"abstract":"In the main result of this paper we prove that a codimension one foliation of $mathbb{P}^n$, which is locally a product near every point of some codimension two component of the singular set, has a Kupka component. In particular, we obtain a generalization of a known result of Calvo Andrade and Brunella about foliations with a Kupka component.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124526450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type Hessian型Enriques曲面和Coble曲面的四面体和自同构
Annales Henri Lebesgue Pub Date : 2018-09-20 DOI: 10.5802/ahl.57
Daniel Allcock, I. Dolgachev
{"title":"The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type","authors":"Daniel Allcock, I. Dolgachev","doi":"10.5802/ahl.57","DOIUrl":"https://doi.org/10.5802/ahl.57","url":null,"abstract":"Consider a cubic surface satisfying the mild condition that it may be described in Sylvester's pentahedral form. There is a well-known Enriques or Coble surface S with K3 cover birationally isomorphic to the Hessian surface of this cubic surface. We describe the nef cone and the (-2)-curves of S. In the case of pentahedral parameters (1, 1, 1, 1, nonzero t) we compute the automorphism group of S. For t not 1 it is the semidirect product of the free product (Z/2)*(Z/2)*(Z/2)*(Z/2) by the symmetric group S4. In the special case t=1/16 we study the action of Aut(S) on an invariant smooth rational curve C on the Coble surface S. We describe the action and its image, both geometrically and arithmetically. In particular, we prove that Aut(S)-->Aut(C) is injective in characteristic 0 and we identify its image with the subgroup of PGL2 coming from the symmetries of a regular tetrahedron and the reflections across its facets.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124805712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A radius 1 irreducibility criterion for lattices in products of trees 树积格的半径1不可约准则
Annales Henri Lebesgue Pub Date : 2018-08-23 DOI: 10.5802/ahl.132
P. Caprace
{"title":"A radius 1 irreducibility criterion for lattices in products of trees","authors":"P. Caprace","doi":"10.5802/ahl.132","DOIUrl":"https://doi.org/10.5802/ahl.132","url":null,"abstract":"Let $T_1, T_2$ be regular trees of degrees $d_1, d_2 geq 3$. Let also $Gamma leq mathrm{Aut}(T_1) times mathrm{Aut}(T_2)$ be a group acting freely and transitively on $VT_1 times VT_2$. For $i=1$ and $2$, assume that the local action of $Gamma$ on $T_i$ is $2$-transitive; if moreover $d_i geq 7$, assume that the local action contains $mathrm{Alt}(d_i)$. We show that $Gamma$ is irreducible, unless $(d_1, d_2)$ belongs to an explicit small set of exceptional values. This yields an irreducibility criterion for $Gamma$ that can be checked purely in terms of its local action on a ball of radius $1$ in $T_1$ and $T_2$. Under the same hypotheses, we show moreover that if $Gamma$ is irreducible, then it is hereditarily just-infinite, provided the local action on $T_i$ is not the affine group $mathbf F_5 rtimes mathbf F_5^*$. The proofs rely, in several ways, on the Classification of the Finite Simple Groups.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121013282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Maps from K-trivial varieties and connectedness problems k -平凡变种的映射与连通性问题
Annales Henri Lebesgue Pub Date : 2018-08-03 DOI: 10.5802/AHL.38
Vladimir Lazi'c, T. Peternell
{"title":"Maps from K-trivial varieties and connectedness problems","authors":"Vladimir Lazi'c, T. Peternell","doi":"10.5802/AHL.38","DOIUrl":"https://doi.org/10.5802/AHL.38","url":null,"abstract":"In this paper we study varieties covered by rational or elliptic curves. First, we show that images of Calabi-Yau or irreducible symplectic varieties under rational maps are almost always rationally connected. Second, we investigate elliptically connected and elliptically chain connected varieties, and varieties swept out by a family of elliptic curves. Among other things, we show that Calabi-Yau or hyperk\"ahler manifolds which are covered by a family of elliptic curves contain uniruled divisors and that elliptically chain connected varieties of dimension at least two contain a rational curve, and so do K-trivial varieties with finite fundamental group which are covered by elliptic curves.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128767171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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