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Annales Henri Lebesgue最新文献

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Disorder and denaturation transition in the generalized Poland–Scheraga model 广义Poland-Scheraga模型中的无序和变性转变
Annales Henri Lebesgue Pub Date : 2018-07-30 DOI: 10.5802/ahl.34
Q. Berger, G. Giacomin, Mahafroz Khatib
{"title":"Disorder and denaturation transition in the generalized Poland–Scheraga model","authors":"Q. Berger, G. Giacomin, Mahafroz Khatib","doi":"10.5802/ahl.34","DOIUrl":"https://doi.org/10.5802/ahl.34","url":null,"abstract":"We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are allowed to be non-complementary (and to have different lengths). The homogeneous model was recently studied from a mathematical point of view in Giacomin, Khatib (Stoch. Proc. Appl., 2017), via a $2$-dimensional renewal approach, with a loop exponent $2+alpha$ (${alpha>0}$): it was found to undergo a localization/delocalization phase transition of order $nu = min(1,alpha)^{-1}$, together with -- in general -- other phase transitions. In this paper, we turn to the disordered model, and we address the question of the influence of disorder on the denaturation phase transition, that is whether adding an arbitrarily small amount of disorder (i.e. inhomogeneities) affects the critical properties of this transition. Our results are consistent with Harris' predictions for $d$-dimensional disordered systems (here $d=2$). First, we prove that when $alpha d/2$), then disorder is irrelevant: the quenched and annealed critical points are equal, and the disordered denaturation phase transition is also of order $nu=alpha^{-1}$. On the other hand, when $alpha>1$, disorder is relevant: we prove that the quenched and annealed critical points differ. \u0000Moreover, we discuss a number of open problems, in particular the smoothing phenomenon that is expected to enter the game when disorder is relevant.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116638174","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
On a gateway between continuous and discrete Bessel and Laguerre processes 关于连续和离散贝塞尔和拉盖尔过程之间的通道
Annales Henri Lebesgue Pub Date : 2018-07-25 DOI: 10.5802/AHL.13
L. Miclo, P. Patie
{"title":"On a gateway between continuous and discrete Bessel and Laguerre processes","authors":"L. Miclo, P. Patie","doi":"10.5802/AHL.13","DOIUrl":"https://doi.org/10.5802/AHL.13","url":null,"abstract":"By providing instances of approximation of linear diffusions by birth-death processes, Feller [13], has offered an original path from the discrete world to the continuous one. In this paper, by identifying an intertwining relationship between squared Bessel processes and some linear birth-death processes, we show that this connection is in fact more intimate and goes in the two directions. As by-products, we identify some properties enjoyed by the birth-death family that are inherited from squared Bessel processes. For instance, these include a discrete self-similarity property and a discrete analogue of the beta-gamma algebra. We proceed by explaining that the same gateway identity also holds for the corresponding ergodic Laguerre semi-groups. It follows again that the continuous and discrete versions are more closely related than thought before, and this enables to pass information from one semi-group to the other one.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130396573","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: 7
Simple connectivity of Fargues–Fontaine curves 法格-方丹曲线的简单连通性
Annales Henri Lebesgue Pub Date : 2018-06-29 DOI: 10.5802/ahl.101
K. Kedlaya
{"title":"Simple connectivity of Fargues–Fontaine curves","authors":"K. Kedlaya","doi":"10.5802/ahl.101","DOIUrl":"https://doi.org/10.5802/ahl.101","url":null,"abstract":"We show that the Fargues--Fontaine curve associated to an algebraically closed field of characteristic p is geometrically simply connected; that is, its base extension from Q_p to any complete algebraically closed overfield admits no nontrivial connected finite etale covering. We then deduce from this an analogue for perfectoid spaces (and some related objects) of Drinfeld's lemma on the fundamental group of a product of schemes in characteristic p.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128444085","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
Generalized eigenvalue methods for Gaussian quadrature rules 高斯正交规则的广义特征值方法
Annales Henri Lebesgue Pub Date : 2018-05-30 DOI: 10.5802/ahl.62
Grigoriy Blekherman, Mario Kummer, C. Riener, M. Schweighofer, C. Vinzant
{"title":"Generalized eigenvalue methods for Gaussian quadrature rules","authors":"Grigoriy Blekherman, Mario Kummer, C. Riener, M. Schweighofer, C. Vinzant","doi":"10.5802/ahl.62","DOIUrl":"https://doi.org/10.5802/ahl.62","url":null,"abstract":"A quadrature rule of a measure $mu$ on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against $mu$ for all polynomials up to some fixed degree. In this paper, we present a bivariate polynomial whose roots parametrize the nodes of minimal quadrature rules for measures on the real line. We give two symmetric determinantal formulas for this polynomial, which translate the problem of finding the nodes to solving a generalized eigenvalue problem.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121826792","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: 0
$ell ^p$-improving for discrete spherical averages $ well ^p$-改进离散球面平均
Annales Henri Lebesgue Pub Date : 2018-04-24 DOI: 10.5802/ahl.50
Kevin A. Hughes
{"title":"$ell ^p$-improving for discrete spherical averages","authors":"Kevin A. Hughes","doi":"10.5802/ahl.50","DOIUrl":"https://doi.org/10.5802/ahl.50","url":null,"abstract":"In this paper, we prove $ell^p$-improving estimates for the discrete spherical averages and some of their generalizations. At first glance this problem appears trivial, but upon further examination we obtain interesting, nontrivial bounds. As an application we give a new estimate for the discrete spherical maximal function in four dimensions. We conclude by introducing a principle to describe the analogy with Littman's result for continuous spherical averages.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134000086","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: 17
Holomorphic volume forms on representation varieties of surfaces with boundary 具有边界的曲面的表示变化上的全纯体积形式
Annales Henri Lebesgue Pub Date : 2018-04-18 DOI: 10.5802/ahl.35
M. Heusener, J. Porti
{"title":"Holomorphic volume forms on representation varieties of surfaces with boundary","authors":"M. Heusener, J. Porti","doi":"10.5802/ahl.35","DOIUrl":"https://doi.org/10.5802/ahl.35","url":null,"abstract":"For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the other one is the power of the Atiyah-Bott-Goldman symplectic form. We introduce an holomorphic volume form on the space of representations of the circle, so that, for surfaces with boundary, it appears as peripheral term in the generalization of Witten's formula. We compute explicit volume and symplectic forms for some simple surfaces and for the Lie group SL(N,C).","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"220 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122060582","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: 5
On the range of a two-dimensional conditioned simple random walk 范围上的二维条件简单随机游走
Annales Henri Lebesgue Pub Date : 2018-04-01 DOI: 10.5802/ahl.20
N. Gantert, S. Popov, M. Vachkovskaia
{"title":"On the range of a two-dimensional conditioned simple random walk","authors":"N. Gantert, S. Popov, M. Vachkovskaia","doi":"10.5802/ahl.20","DOIUrl":"https://doi.org/10.5802/ahl.20","url":null,"abstract":"We consider the two-dimensional simple random walk conditioned on never hitting the origin. This process is a Markov chain, namely it is the Doob $h$-transform of the simple random walk with respect to the potential kernel. It is known to be transient and we show that it is \"almost recurrent\" in the sense that each infinite set is visited infinitely often, almost surely. We prove that, for a \"large\" set, the proportion of its sites visited by the conditioned walk is approximately a Uniform$[0,1]$ random variable. Also, given a set $Gsubsetmathbb{R}^2$ that does not \"surround\" the origin, we prove that a.s. there is an infinite number of $k$'s such that $kGcap mathbb{Z}^2$ is unvisited. These results suggest that the range of the conditioned walk has \"fractal\" behavior.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"88 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125181263","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
Extensions of partial cyclic orders and consecutive coordinate polytopes 部分循环序和连续坐标多面体的扩展
Annales Henri Lebesgue Pub Date : 2018-03-27 DOI: 10.5802/ahl.33
Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy
{"title":"Extensions of partial cyclic orders and consecutive coordinate polytopes","authors":"Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy","doi":"10.5802/ahl.33","DOIUrl":"https://doi.org/10.5802/ahl.33","url":null,"abstract":"We introduce several classes of polytopes contained in $[0,1]^n$ and cut out by inequalities involving sums of consecutive coordinates, extending a construction by Stanley. We show that the normalized volumes of these polytopes enumerate the extensions to total cyclic orders of certains classes of partial cyclic orders. We also provide a combinatorial interpretation of the Ehrhart $h^*$-polynomials of some of these polytopes in terms of descents of total cyclic orders. The Euler numbers, the Eulerian numbers and the Narayana numbers appear as special cases.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122666227","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
Commensurating actions for groups of piecewise continuous transformations 分段连续变换组的通约动作
Annales Henri Lebesgue Pub Date : 2018-03-22 DOI: 10.5802/ahl.107
Yves Cornulier
{"title":"Commensurating actions for groups of piecewise continuous transformations","authors":"Yves Cornulier","doi":"10.5802/ahl.107","DOIUrl":"https://doi.org/10.5802/ahl.107","url":null,"abstract":"We use partial actions, as formalized by Exel, to construct various commensurating actions. We use this in the context of groups piecewise preserving a geometric structure, and we interpret the transfixing property of these commensurating actions as the existence of a model for which the group acts preserving the geometric structure. We apply this to many groups with piecewise properties in dimension 1, notably piecewise of class C^k, piecewise affine, piecewise projective (possibly discontinuous). \u0000We derive various conjugacy results for subgroups with Property FW, or distorted cyclic subgroups, or more generally in the presence of rigidity properties for commensurating actions. For instance we obtain, under suitable assumptions, the conjugacy of a given piecewise affine action to an affine action on possibly another model. By the same method, we obtain a similar result in the projective case. An illustrating corollary is the fact that the group of piecewise projective self-transformations of the circle has no infinite subgroup with Kazhdan's Property T; this corollary is new even in the piecewise affine case. \u0000In addition, we use this to provide of the classification of circle subgroups of piecewise projective homeomorphisms of the projective line. The piecewise affine case is a classical result of Minakawa.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130067827","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: 11
Wigner measures and effective mass theorems 维格纳测度和有效质量定理
Annales Henri Lebesgue Pub Date : 2018-03-20 DOI: 10.5802/ahl.54
F. Macià, V. Chabu, C. Fermanian-Kammerer
{"title":"Wigner measures and effective mass theorems","authors":"F. Macià, V. Chabu, C. Fermanian-Kammerer","doi":"10.5802/ahl.54","DOIUrl":"https://doi.org/10.5802/ahl.54","url":null,"abstract":"We study a semi-classical Schr{\"o}dinger equation which describes the dynamics of an electron in a crystal in the presence of impurities. It is well-known that under suitable assumptions on the initial data, the wave function can be approximated in the semi-classical limit by the solution of a simpler equation, the effective mass equation. Using Floquet-Bloch decomposition and with a non-degeneracy condition on the critical points of the Bloch bands, as it is classical in this subject, we establish effective mass equations for more general initial data. Then, when the critical points are degenerated (which may occur in dimension strictly larger than one), we prove that a similar analysis can be performed, leading to a new type of effective mass equations which are operator-valued and of Heisenberg form. Our analysis relies on Wigner measure theory and, more precisely, to its applications to the analysis of dispersion effects.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127708146","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: 7
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