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The Expectation of a Multiplicative Functional under the Sine-Process 正弦过程下乘法函数的期望值
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020035
Alexander Bufetov
{"title":"The Expectation of a Multiplicative Functional under the Sine-Process","authors":"Alexander Bufetov","doi":"10.1134/s0016266324020035","DOIUrl":"https://doi.org/10.1134/s0016266324020035","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> An explicit expression for the expected value of a regularized multiplicative functional under the sine-process is obtained by passing to the scaling limit in the Borodin–Okounkov–Geronimo–Case formula. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Continuous Selection of Approximate Monge Solutions in the Kantorovich Problem with a Parameter 带参数的康托洛维奇问题中近似蒙日解的连续选择
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020096
Svetlana Popova
{"title":"Continuous Selection of Approximate Monge Solutions in the Kantorovich Problem with a Parameter","authors":"Svetlana Popova","doi":"10.1134/s0016266324020096","DOIUrl":"https://doi.org/10.1134/s0016266324020096","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge mappings continuous with respect to the parameter. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Conjugacy of Measurable Partitions with Respect to the Normalizer of a Full Type $$mathrm{II}_1$$ Ergodic Group 论相对于全类型 $$mathrm{II}_1$ 尔后组归一化的可测分区的共轭性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020084
Andrei Lodkin, Benzion Rubshtein
{"title":"On the Conjugacy of Measurable Partitions with Respect to the Normalizer of a Full Type $$mathrm{II}_1$$ Ergodic Group","authors":"Andrei Lodkin, Benzion Rubshtein","doi":"10.1134/s0016266324020084","DOIUrl":"https://doi.org/10.1134/s0016266324020084","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>(G)</span> be a countable ergodic group of automorphisms of a measure space <span>((X,mu))</span> and <span>(mathcal{N}[G])</span> be the normalizer of its full group <span>([G])</span>. Problem: for a pair of measurable partitions <span>(xi)</span> and <span>(eta)</span> of the space <span>(X)</span>, when does there exist an element <span>(ginmathcal{N}[G])</span> such that <span>(gxi=eta)</span>? For a wide class of measurable partitions, we give a solution to this problem in the case where <span>(G)</span> is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to <span>(xi)</span> and <span>(eta)</span> in the type <span>(mathrm{II}_1)</span> factor constructed via the orbit partition of the group <span>(G)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Liouville Property and Poisson Boundary of Random Walks with Infinite Entropy: What’s Amiss? 具有无限熵的随机漫步的柳维尔特性和泊松边界：出了什么问题？
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020060
Vadim Kaimanovich
{"title":"Liouville Property and Poisson Boundary of Random Walks with Infinite Entropy: What’s Amiss?","authors":"Vadim Kaimanovich","doi":"10.1134/s0016266324020060","DOIUrl":"https://doi.org/10.1134/s0016266324020060","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We discuss the qualitatively new properties of random walks on groups that arise in the situation when the entropy of the step distribution is infinite. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Miracle of Integer Eigenvalues 整数特征值的奇迹
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020072
Richard Kenyon, Maxim Kontsevich, Oleg Ogievetskii, Cosmin Pohoata, Will Sawin, Semen Shlosman
{"title":"The Miracle of Integer Eigenvalues","authors":"Richard Kenyon, Maxim Kontsevich, Oleg Ogievetskii, Cosmin Pohoata, Will Sawin, Semen Shlosman","doi":"10.1134/s0016266324020072","DOIUrl":"https://doi.org/10.1134/s0016266324020072","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For partially ordered sets <span>((X, preccurlyeq))</span>, we consider the square matrices <span>(M^{X})</span> with rows and columns indexed by linear extensions of the partial order on <span>(X)</span>. Each entry <span>((M^{X})_{PQ})</span> is a formal variable defined by a pedestal of the linear order <span>(Q)</span> with respect to linear order <span>(P)</span>. We show that all eigenvalues of any such matrix <span>(M^{X})</span> are <span>(mathbb{Z})</span>-linear combinations of those variables. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Golden and Silver Stationary Points in Probe Particle Dynamics within a Modular Domain 模块域内探测器粒子动力学中的金银静止点
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020047
Alexander Gorsky, Sergei Nechaev
{"title":"Golden and Silver Stationary Points in Probe Particle Dynamics within a Modular Domain","authors":"Alexander Gorsky, Sergei Nechaev","doi":"10.1134/s0016266324020047","DOIUrl":"https://doi.org/10.1134/s0016266324020047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The flows generated by the iterative dynamics of triangle reflections are analyzed. These flows are interpreted as the adiabatic dynamics of probe particles within the fundamental domain of the modular group. Two specific cases of lattices are considered: (a) those generated by reflections of equilateral triangles, and (b) those generated by reflections of rectangular isosceles triangles. We demonstrate that the stationary points of the flows for equilateral and isosceles triangles correspond to the “Golden” and the “Silver” ratios, respectively. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Duality for the Kantorovich Problem with a Fixed Barycenter and Barycenters of Functionals 具有固定边心和函数边心的康托洛维奇问题的对偶性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020023
Konstantin Afonin
{"title":"Duality for the Kantorovich Problem with a Fixed Barycenter and Barycenters of Functionals","authors":"Konstantin Afonin","doi":"10.1134/s0016266324020023","DOIUrl":"https://doi.org/10.1134/s0016266324020023","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper is devoted to the study of duality in the linear Kantorovich problem with a fixed barycenter. It is proved that Kantorovich duality holds for general lower semicontinuous cost functions on completely regular spaces. In the course of considering this subject, the question of representation of a continuous linear functional by a Radon measure is raised and solved, provided that the barycenter of the functional is given by a Radon measure. In addition, we consider two new barycentric optimization problems and prove duality results for them. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Elliptic Analogue of the Vershik–Kerov Limit Shape Vershik-Kerov 极限形状的椭圆类似物
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020059
Andrei Grekov, Nikita Nekrasov
{"title":"Elliptic Analogue of the Vershik–Kerov Limit Shape","authors":"Andrei Grekov, Nikita Nekrasov","doi":"10.1134/s0016266324020059","DOIUrl":"https://doi.org/10.1134/s0016266324020059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a <span>(U(1))</span> case of <span>(mathcal{N}=2^{*})</span> gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Anatoly Moiseevich Vershik (1933–2024) 阿纳托利-莫伊谢耶维奇-韦尔希克（1933-2024）
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/s0016266324020011
{"title":"Anatoly Moiseevich Vershik (1933–2024)","authors":"","doi":"10.1134/s0016266324020011","DOIUrl":"https://doi.org/10.1134/s0016266324020011","url":null,"abstract":"","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Grothendieck Ring of Pairs of Quasi-Projective Varieties 准投影变项对的格罗根迪克环
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/s0016266324010040
Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández
{"title":"Grothendieck Ring of Pairs of Quasi-Projective Varieties","authors":"Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández","doi":"10.1134/s0016266324010040","DOIUrl":"https://doi.org/10.1134/s0016266324010040","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe <span>(lambda)</span>-structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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