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Algebraic groups in non-commutative probability theory revisited 非交换概率论中的代数群再论
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2024-05-29 DOI: 10.1142/s021902572450005x
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
{"title":"Algebraic groups in non-commutative probability theory revisited","authors":"Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras","doi":"10.1142/s021902572450005x","DOIUrl":"https://doi.org/10.1142/s021902572450005x","url":null,"abstract":"<p>The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie calculus, and results in another construction of groups of characters encoding the behavior of states. Comparing the two, the first approach, recast recently in a general categorical language by Manzel and Schürmann, can be seen as largely driven by the theory of universal products, whereas the second construction builds on Hopf algebras and a suitable algebraization of the combinatorics of non-crossing set partitions. Although both address the same phenomena, moving between the two viewpoints is not obvious. We present here an attempt to unify the two approaches by making explicit the Hopf algebraic connections between them. Our presentation, although relying largely on classical ideas as well as results closely related to Manzel and Schürmann’s aforementioned work, is nevertheless original on several points and fills a gap in the non-commutative probability literature. In particular, we systematically use the language and techniques of algebraic groups together with shuffle group techniques to prove that two notions of algebraic groups naturally associated with free, respectively, Boolean and monotone, probability theories identify. We also obtain explicit formulas for various Hopf algebraic structures and detail arguments that had been left implicit in the literature.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258509","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
A lower bound estimate of life span of solutions to stochastic 3D Navier–Stokes equations with convolution-type noise 具有卷积型噪声的随机三维纳维-斯托克斯方程解的寿命下限估计
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2024-04-24 DOI: 10.1142/s0219025724500024
Siyu Liang
{"title":"A lower bound estimate of life span of solutions to stochastic 3D Navier–Stokes equations with convolution-type noise","authors":"Siyu Liang","doi":"10.1142/s0219025724500024","DOIUrl":"https://doi.org/10.1142/s0219025724500024","url":null,"abstract":"<p>In this paper, we investigate the stochastic 3D Navier–Stokes equations perturbed by linear multiplicative Gaussian noise of convolution type by transformation to random PDEs. We focus on obtaining bounds from below for the life span associated with regular initial data. The key point of the proof is the fixed point argument.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801193","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
Dissipative dynamics for infinite lattice systems 无限晶格系统的耗散动力学
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2024-03-11 DOI: 10.1142/s0219025723500303
Shreya Mehta, Boguslaw Zegarlinski
{"title":"Dissipative dynamics for infinite lattice systems","authors":"Shreya Mehta, Boguslaw Zegarlinski","doi":"10.1142/s0219025723500303","DOIUrl":"https://doi.org/10.1142/s0219025723500303","url":null,"abstract":"<p>We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an idea of quasi-invariance of a state, we show how one can construct unitary representations of various groups. Moreover in models with locally conserved quantities associated to an infinite lattice we show that there is no spectral gap and the corresponding dissipative dynamics decay to equilibrium polynomially in time.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105812","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
Combinatorial aspects of weighted free Poisson random variables 加权自由泊松随机变量的组合问题
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2024-02-17 DOI: 10.1142/s0219025724500012
Nobuhiro Asai, Hiroaki Yoshida
{"title":"Combinatorial aspects of weighted free Poisson random variables","authors":"Nobuhiro Asai, Hiroaki Yoshida","doi":"10.1142/s0219025724500012","DOIUrl":"https://doi.org/10.1142/s0219025724500012","url":null,"abstract":"<p>This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106376","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 near-martingales and a class of anticipating linear stochastic differential equations 关于近马丁格尔和一类预期线性随机微分方程
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-12-16 DOI: 10.1142/s0219025723500297
Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha, Padmanabhan Sundar
{"title":"On near-martingales and a class of anticipating linear stochastic differential equations","authors":"Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha, Padmanabhan Sundar","doi":"10.1142/s0219025723500297","DOIUrl":"https://doi.org/10.1142/s0219025723500297","url":null,"abstract":"<p>The goals of this paper are to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. For a class of anticipating linear stochastic differential equations, we prove the existence and uniqueness of solutions using two approaches: (1) Ayed–Kuo differential formula using an ansatz, and (2) a braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin–Wentzell type large deviations result for the solution of such equations. In addition, we prove large deviation results for small noise where the initial conditions are random.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106380","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
Hamiltonian of Free Field on Infinite-Dimensional Hypercube 无限维超立方体上自由场的哈密顿量
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-07 DOI: 10.1142/s0219025723500273
Lixia Zhang, Caishi Wang
{"title":"Hamiltonian of Free Field on Infinite-Dimensional Hypercube","authors":"Lixia Zhang, Caishi Wang","doi":"10.1142/s0219025723500273","DOIUrl":"https://doi.org/10.1142/s0219025723500273","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135541282","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
Quantum Properties of Classical Pearson Random Variables 经典皮尔逊随机变量的量子特性
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-07 DOI: 10.1142/s0219025723500285
Luigi Accardi, Abdon Ebang Ella, Un Cig Ji, Yun Gang Lu
{"title":"Quantum Properties of Classical Pearson Random Variables","authors":"Luigi Accardi, Abdon Ebang Ella, Un Cig Ji, Yun Gang Lu","doi":"10.1142/s0219025723500285","DOIUrl":"https://doi.org/10.1142/s0219025723500285","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135541280","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
An infinite-dimensional non-linear equation related to gibbs measures of a sos model 一个与sos模型的吉布斯测度有关的无限维非线性方程
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-04 DOI: 10.1142/s0219025723500261
U. A. Rozikov
{"title":"An infinite-dimensional non-linear equation related to gibbs measures of a sos model","authors":"U. A. Rozikov","doi":"10.1142/s0219025723500261","DOIUrl":"https://doi.org/10.1142/s0219025723500261","url":null,"abstract":"For the solid-on-solid (SOS) model with an external field and with spin values from the set of all integers on a Cayley tree, each (gradient) Gibbs measure corresponds to a boundary law (an infinite-dimensional vector function defined on vertices of the Cayley tree) satisfying a nonlinear functional equation. Recently some translation-invariant and height-periodic (non-normalizable) solutions to the equation are found. Here, our aim is to find non-height-periodic and non-normalizable boundary laws for the SOS model. By such a solution one can construct a non-probability Gibbs measure. We find explicitly several non-normalizable boundary laws. Moreover, we reduce the problem to solving of a nonlinear, second-order difference equation. We give analytic and numerical analyses of the difference equation.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728311","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
HOLOGRAPHIC PHOTOSYNTHESIS AND ENTANGLEMENT ENTROPY 全息光合作用和纠缠熵
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0019
IRINA AREF’EVA, IGOR VOLOVICH
{"title":"HOLOGRAPHIC PHOTOSYNTHESIS AND ENTANGLEMENT ENTROPY","authors":"IRINA AREF’EVA, IGOR VOLOVICH","doi":"10.1142/9789811275999_0019","DOIUrl":"https://doi.org/10.1142/9789811275999_0019","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514898","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
BASINS OF ATTRACTION OF INVARIANT STATES OF A QUANTUM MARKOV SEMIGROUP 量子马尔可夫半群不变态的吸引盆地
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0004
F. FAGNOLA, E. SASSO, V. UMANITA
{"title":"BASINS OF ATTRACTION OF INVARIANT STATES OF A QUANTUM MARKOV SEMIGROUP","authors":"F. FAGNOLA, E. SASSO, V. UMANITA","doi":"10.1142/9789811275999_0004","DOIUrl":"https://doi.org/10.1142/9789811275999_0004","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515100","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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