发布求助
文献互助 智能选刊 最新文献

Probability Theory and Related Fields最新文献

筛选
英文 中文
Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space 带有乘法空间白噪声的二维非线性薛定谔方程在全空间上的全局好求解性
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-06-22 DOI: 10.1007/s00440-024-01288-y
Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia
{"title":"Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space","authors":"Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia","doi":"10.1007/s00440-024-01288-y","DOIUrl":"https://doi.org/10.1007/s00440-024-01288-y","url":null,"abstract":"<p>We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labbé (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"27 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507312","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
Geometry of Gaussian free field sign clusters and random interlacements 高斯自由场符号集群和随机交错的几何形状
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-06-15 DOI: 10.1007/s00440-024-01285-1
Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
{"title":"Geometry of Gaussian free field sign clusters and random interlacements","authors":"Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez","doi":"10.1007/s00440-024-01285-1","DOIUrl":"https://doi.org/10.1007/s00440-024-01285-1","url":null,"abstract":"<p>For a large class of amenable transient weighted graphs <i>G</i>, we prove that the sign clusters of the Gaussian free field on <i>G</i> fall into a regime of <i>strong supercriticality</i>, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with overwhelming probability. Examples of graphs belonging to this class include regular lattices such as <span>({mathbb {Z}}^d)</span>, for <span>(dge 3)</span>, but also more intricate geometries, such as Cayley graphs of suitably growing (finitely generated) non-Abelian groups, and cases in which random walks exhibit anomalous diffusive behavior, for instance various fractal graphs. As a consequence, we also show that the vacant set of random interlacements on these objects, introduced by Sznitman (Ann Math 171(3):2039–2087, 2010), and which is intimately linked to the free field, contains an infinite connected component at small intensities. In particular, this result settles an open problem from Sznitman (Invent Math 187(3):645–706, 2012).</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"54 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507313","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
Characterizing models in regularity structures: a quasilinear case 正则结构中的模型特征：准线性案例
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-06-07 DOI: 10.1007/s00440-024-01292-2
Markus Tempelmayr
{"title":"Characterizing models in regularity structures: a quasilinear case","authors":"Markus Tempelmayr","doi":"10.1007/s00440-024-01292-2","DOIUrl":"https://doi.org/10.1007/s00440-024-01292-2","url":null,"abstract":"<p>We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we believe that the method is robust and applies to a much broader class of subcritical equations. Furthermore, we prove that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies the corresponding convergence of the associated models. Combined with the characterization, this establishes a universality-type result.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"64 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550772","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
Benign overfitting and adaptive nonparametric regression 良性过拟合和自适应非参数回归
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-06-06 DOI: 10.1007/s00440-024-01278-0
Julien Chhor, Suzanne Sigalla, Alexandre B. Tsybakov
{"title":"Benign overfitting and adaptive nonparametric regression","authors":"Julien Chhor, Suzanne Sigalla, Alexandre B. Tsybakov","doi":"10.1007/s00440-024-01278-0","DOIUrl":"https://doi.org/10.1007/s00440-024-01278-0","url":null,"abstract":"<p>We study benign overfitting in the setting of nonparametric regression under mean squared risk, and on the scale of Hölder classes. We construct a local polynomial estimator of the regression function that is minimax optimal on a Hölder class with any given smoothness, and that is a continuous function interpolating the set of observations with high probability. The key element of the construction is the use of singular kernels. Moreover, we prove that adaptation to unknown smoothness is compatible with benign overfitting. Namely, we construct a continuous and interpolating local polynomial estimator attaining the minimax optimal rate in <span>(L_2)</span> adaptively to the unknown Hölder smoothness. Our results highlight the fact that interpolation can be fundamentally decoupled from bias-variance tradeoff in the problem of nonparametric regression.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550773","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
Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes 通过径向 Dunkl 过程的大偏差实现广义贝塞尔函数和权重乘数的渐近性
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-05-19 DOI: 10.1007/s00440-024-01282-4
Jiaoyang Huang, Colin McSwiggen
{"title":"Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes","authors":"Jiaoyang Huang, Colin McSwiggen","doi":"10.1007/s00440-024-01282-4","DOIUrl":"https://doi.org/10.1007/s00440-024-01282-4","url":null,"abstract":"<p>This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature implies a large deviations principle for the hydrodynamic limit of radial Dunkl processes. Using this fact, we prove a variational formula for the large-<i>N</i> asymptotics of generalized Bessel functions, as well as a large deviations principle for the more general family of radial Heckman–Opdam processes. As an application, we prove a theorem on the asymptotic behavior of weight multiplicities of irreducible representations of compact or complex simple Lie algebras in the limit of large rank. The theorems in this paper generalize several known results describing analogous asymptotics for Dyson Brownian motion, spherical matrix integrals, and Kostka numbers.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146390","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 Brownian transport map 布朗运动图
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-05-16 DOI: 10.1007/s00440-024-01286-0
Dan Mikulincer, Yair Shenfeld
{"title":"The Brownian transport map","authors":"Dan Mikulincer, Yair Shenfeld","doi":"10.1007/s00440-024-01286-0","DOIUrl":"https://doi.org/10.1007/s00440-024-01286-0","url":null,"abstract":"<p>Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the Föllmer process, which pushes forward the Wiener measure onto probability measures on Euclidean spaces. Utilizing the tools of the Malliavin and stochastic calculus in Wiener space, we show that this Brownian transport map is a contraction in various settings where the analogous questions for optimal transport maps are open. The contraction properties of the Brownian transport map enable us to prove functional inequalities in Euclidean spaces, which are either completely new or improve on current results. Further and related applications of our contraction results are the existence of Stein kernels with desirable properties (which lead to new central limit theorems), as well as new insights into the Kannan–Lovász–Simonovits conjecture. We go beyond the Euclidean setting and address the problem of contractions on the Wiener space itself. We show that optimal transport maps and causal optimal transport maps (which are related to Brownian transport maps) between the Wiener measure and other target measures on Wiener space exhibit very different behaviors.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"68 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060038","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
Inhomogeneous long-range percolation in the weak decay regime 弱衰变体系中的非均质长程渗流
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-05-15 DOI: 10.1007/s00440-024-01281-5
Christian Mönch
{"title":"Inhomogeneous long-range percolation in the weak decay regime","authors":"Christian Mönch","doi":"10.1007/s00440-024-01281-5","DOIUrl":"https://doi.org/10.1007/s00440-024-01281-5","url":null,"abstract":"<p>We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the <i>weak decay regime</i>, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"131 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060039","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
Minimal distance between random orbits 随机轨道之间的最小距离
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-05-11 DOI: 10.1007/s00440-024-01283-3
Sébastien Gouëzel, Jérôme Rousseau, Manuel Stadlbauer
{"title":"Minimal distance between random orbits","authors":"Sébastien Gouëzel, Jérôme Rousseau, Manuel Stadlbauer","doi":"10.1007/s00440-024-01283-3","DOIUrl":"https://doi.org/10.1007/s00440-024-01283-3","url":null,"abstract":"<p>We study the minimal distance between two orbit segments of length <i>n</i>, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called correlation dimension (or Rényi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"8 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929907","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
Infinite disorder renormalization fixed point for the continuum random field Ising chain 连续随机场伊辛链的无限无序重正化定点
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-04-29 DOI: 10.1007/s00440-024-01284-2
Orphée Collin, Giambattista Giacomin, Yueyun Hu
{"title":"Infinite disorder renormalization fixed point for the continuum random field Ising chain","authors":"Orphée Collin, Giambattista Giacomin, Yueyun Hu","doi":"10.1007/s00440-024-01284-2","DOIUrl":"https://doi.org/10.1007/s00440-024-01284-2","url":null,"abstract":"<p>We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (<i>domain-wall structure</i>). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the <i>infinite disorder fixed point</i> process introduced by D. S. Fisher in the context of zero temperature quantum Ising chains. In particular, our results establish a number of predictions that one can find in Fisher et al. (Phys Rev E 64:41, 2001). The infinite disorder fixed point process for centered external field is equivalently described in terms of the process of <i>suitably selected</i> extrema of a Brownian trajectory introduced and studied by Neveu and Pitman (in: Séminaire de probabilités XXIII. Lecture notes in mathematics, vol 1372, pp 239–247, 1989). This characterization of the infinite disorder fixed point is one of the important ingredients of our analysis.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"44 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838222","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
Average-case analysis of the Gaussian elimination with partial pivoting 带部分支点的高斯消元的平均情况分析
IF 2 1区 数学
Probability Theory and Related Fields Pub Date : 2024-04-22 DOI: 10.1007/s00440-024-01276-2
Han Huang, Konstantin Tikhomirov
{"title":"Average-case analysis of the Gaussian elimination with partial pivoting","authors":"Han Huang, Konstantin Tikhomirov","doi":"10.1007/s00440-024-01276-2","DOIUrl":"https://doi.org/10.1007/s00440-024-01276-2","url":null,"abstract":"<p>The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for a <i>typical</i> square coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random <span>(ntimes n)</span> standard Gaussian coefficient matrix <i>A</i>, the <i>growth factor</i> of the Gaussian elimination with partial pivoting is at most polynomially large in <i>n</i> with probability close to one. This implies that with probability close to one the number of bits of precision sufficient to solve <span>(Ax = b)</span> to <i>m</i> bits of accuracy using GEPP is <span>(m+O(log n))</span>, which improves an earlier estimate <span>(m+O(log ^2 n))</span> of Sankar, and which we conjecture to be optimal by the order of magnitude. We further provide tail estimates of the growth factor which can be used to support the empirical observation that GEPP is more stable than the Gaussian Elimination with no pivoting.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"82 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803415","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
首页 上一页 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