001482742 000__ 04736cam\\22006377i\4500
001482742 001__ 1482742
001482742 003__ OCoLC
001482742 005__ 20231128003349.0
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001482742 008__ 231031s2023\\\\sz\\\\\\ob\\\\001\0\eng\d
001482742 019__ $$a1406407990$$a1406409262
001482742 020__ $$a9783031433320$$q(electronic bk.)
001482742 020__ $$a3031433327$$q(electronic bk.)
001482742 020__ $$z9783031433313
001482742 020__ $$z3031433319
001482742 0247_ $$a10.1007/978-3-031-43332-0$$2doi
001482742 035__ $$aSP(OCoLC)1406982674
001482742 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX$$dEBLCP$$dYDX$$dOCLCO
001482742 049__ $$aISEA
001482742 050_4 $$aQA273.67$$b.C44 2023
001482742 08204 $$a519.2$$223/eng/20231031
001482742 1001_ $$aChen, Zhen-Qing,$$eauthor.
001482742 24510 $$aLimit theorems for some long range random walks on torsion free nilpotent groups /$$cZhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng.
001482742 264_1 $$aCham :$$bSpringer,$$c2023.
001482742 300__ $$a1 online resource (xiii, 139 pages).
001482742 336__ $$atext$$btxt$$2rdacontent
001482742 337__ $$acomputer$$bc$$2rdamedia
001482742 338__ $$aonline resource$$bcr$$2rdacarrier
001482742 4901_ $$aSpringerBriefs in mathematics,$$x2191-8201
001482742 504__ $$aIncludes bibliographical references and index.
001482742 5050_ $$aIntro -- Preface -- Acknowledgments -- Contents -- 1 Setting the Stage -- 1.1 Review of Some Abelian Results -- 1.2 Illustrative Examples on Nilpotent Matrix Groups -- Notation -- 2 Introduction -- 2.1 Basic Question -- 2.2 Description of the Basic Ingredients and Results -- 2.3 Detailed Description of Some Special Cases -- 2.3.1 Word Length Radial Stable Walks -- 2.3.2 Walks Taking Stable-Like Steps Along One-Parameter Subgroups -- 2.3.3 Walks Associated with Measure in SM() -- 2.4 Symmetric Continuous Convolution Semigroup of Probability Measures and Lévy Processes -- 2.5 Prior Results
001482742 5058_ $$a2.5.1 Functional Type Limit Theorems -- 2.5.2 Local Limit Theorems -- 3 Polynomial Coordinates and Approximate Dilations -- 3.1 Polynomial Coordinate Systems -- 3.2 Dilations, Approximate Dilations, and Limit Groups -- 3.2.1 Straight Dilations -- 3.2.2 Approximate Group Dilations and Limit Groups -- 4 Vague Convergence and Change of Group Law -- 4.1 Vague Convergence Under Rescaling -- 4.2 Vague Convergence of Jump Measures and Kernels -- 5 Weak Convergence of the Processes -- 5.1 Assumption (A) -- 5.2 Geometries on Rd and G -- 5.3 Convergence of Volume -- 5.4 Further Hypotheses
001482742 5058_ $$a5.4.1 The Random Walk on (Regularity) -- 5.4.2 Exit Time Estimates -- 5.4.3 Tails Properties for Jt and J -- 5.5 Weak Convergence -- 5.6 Proof of Theorem 5.11 -- 6 Local Limit Theorem -- 6.1 Assumption (R2) -- 6.2 Statement and Proof of the LLT -- 7 Symmetric Lévy Processes on Nilpotent Groups -- 7.1 The Problem of Identifying the Limit Process -- 7.2 Symmetric Lévy Processes and Their Approximations -- 7.3 Examples -- 8 Measures in SM() and Their Geometries -- 8.1 Probability Measures in SM and SM1 -- 8.2 Weight Systems on Associated with Measures in SM()
001482742 506__ $$aAccess limited to authorized users.
001482742 520__ $$aThis book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.
001482742 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 30, 2023).
001482742 650_6 $$aThéorèmes limites (Théorie des probabilités)
001482742 650_6 $$aMarches aléatoires (Mathématiques)
001482742 650_0 $$aLimit theorems (Probability theory)
001482742 650_0 $$aRandom walks (Mathematics)$$0(DLC)sh 85111357
001482742 655_0 $$aElectronic books.
001482742 7001_ $$aKumagai, Takashi,$$eauthor.
001482742 7001_ $$aSaloff-Coste, L.,$$eauthor.
001482742 7001_ $$aWang, Jian$$c(Mathematician),$$eauthor.$$d1956-$$0(OCoLC)oca07849984
001482742 7001_ $$aZheng, Tianyi,$$eauthor.
001482742 77608 $$iPrint version: $$z3031433319$$z9783031433313$$w(OCoLC)1391916736
001482742 830_0 $$aSpringerBriefs in mathematics,$$x2191-8201
001482742 852__ $$bebk
001482742 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-43332-0$$zOnline Access$$91397441.1
001482742 909CO $$ooai:library.usi.edu:1482742$$pGLOBAL_SET
001482742 980__ $$aBIB
001482742 980__ $$aEBOOK
001482742 982__ $$aEbook
001482742 983__ $$aOnline
001482742 994__ $$a92$$bISE