{"title":"多项式有限自由乘法卷积根的大数定律","authors":"Katsunori Fujie, Yuki Ueda","doi":"10.3842/SIGMA.2023.004","DOIUrl":null,"url":null,"abstract":"We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials which have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution when their degree tends to infinity.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials\",\"authors\":\"Katsunori Fujie, Yuki Ueda\",\"doi\":\"10.3842/SIGMA.2023.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials which have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution when their degree tends to infinity.\",\"PeriodicalId\":49453,\"journal\":{\"name\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3842/SIGMA.2023.004\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3842/SIGMA.2023.004","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials
We provide the law of large numbers for roots of finite free multiplicative convolution of polynomials which have only non-negative real roots. Moreover, we study the empirical root distributions of limit polynomials obtained through the law of large numbers of finite free multiplicative convolution when their degree tends to infinity.
期刊介绍:
Scope
Geometrical methods in mathematical physics
Lie theory and differential equations
Classical and quantum integrable systems
Algebraic methods in dynamical systems and chaos
Exactly and quasi-exactly solvable models
Lie groups and algebras, representation theory
Orthogonal polynomials and special functions
Integrable probability and stochastic processes
Quantum algebras, quantum groups and their representations
Symplectic, Poisson and noncommutative geometry
Algebraic geometry and its applications
Quantum field theories and string/gauge theories
Statistical physics and condensed matter physics
Quantum gravity and cosmology.