東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Random walks on infinite groups

Lalley, Steven P.

FindBook

Google Book

Amazon

博客來

Random walks on infinite groups

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Random walks on infinite groups/ by Steven P. Lalley.
作者:	Lalley, Steven P.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	1 online resource (xii, 369 p.) :ill., digital ;24 cm.
內容註:	1 First Steps -- 2 The Ergodic Theorem -- 3 Subadditivity and its Ramifications -- 4 The Carne-Varopoulos Inequality -- 5 Isoperimetric Inequalities and Amenability -- 6 Markov Chains and Harmonic Functions -- 7 Dirichlet's Principle and the Recurrence Type Theorem -- 8 Martingales -- 9 Bounded Harmonic Functions -- 10 Entropy -- 11 Compact Group Actions and Boundaries -- 12 Poisson Boundaries -- 13 Hyperbolic Groups -- 14 Unbounded Harmonic Functions -- 15 Groups of Polynomial Growth -- Appendix A: A 57-Minute Course in Measure-Theoretic Probability.
Contained By:	Springer Nature eBook
標題:	Random walks (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-25632-5
ISBN:	9783031256325

Random walks on infinite groups
Lalley, Steven P.

Random walks on infinite groups[electronic resource] /by Steven P. Lalley. - Cham :Springer International Publishing :2023. - 1 online resource (xii, 369 p.) :ill., digital ;24 cm. - Graduate texts in mathematics,2972197-5612 ;. - Graduate texts in mathematics ;297..

1 First Steps -- 2 The Ergodic Theorem -- 3 Subadditivity and its Ramifications -- 4 The Carne-Varopoulos Inequality -- 5 Isoperimetric Inequalities and Amenability -- 6 Markov Chains and Harmonic Functions -- 7 Dirichlet's Principle and the Recurrence Type Theorem -- 8 Martingales -- 9 Bounded Harmonic Functions -- 10 Entropy -- 11 Compact Group Actions and Boundaries -- 12 Poisson Boundaries -- 13 Hyperbolic Groups -- 14 Unbounded Harmonic Functions -- 15 Groups of Polynomial Growth -- Appendix A: A 57-Minute Course in Measure-Theoretic Probability.

This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.

ISBN: 9783031256325

Standard No.: 10.1007/978-3-031-25632-5doiSubjects--Topical Terms:

532102
Random walks (Mathematics)

LC Class. No.: QA274.73

Dewey Class. No.: 519.282

Random walks on infinite groups
LDR:02766nmm a2200361 a 4500 001 2318965
003 DE-He213
005 20230508140540.0
006 m d
007 cr nn 008maaau
008 230902s2023 sz s 0 eng d
020 $a 9783031256325 $q (electronic bk.)
020 $a 9783031256318 $q (paper)
024 7 $a 10.1007/978-3-031-25632-5 $2 doi
035 $a 978-3-031-25632-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.73
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.282 $2 23
090 $a QA274.73 $b .L197 2023
100 1 $a Lalley, Steven P. $3 3634471
245 1 0 $a Random walks on infinite groups $h [electronic resource] / $c by Steven P. Lalley.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a 1 online resource (xii, 369 p.) : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 297
505 0 $a 1 First Steps -- 2 The Ergodic Theorem -- 3 Subadditivity and its Ramifications -- 4 The Carne-Varopoulos Inequality -- 5 Isoperimetric Inequalities and Amenability -- 6 Markov Chains and Harmonic Functions -- 7 Dirichlet's Principle and the Recurrence Type Theorem -- 8 Martingales -- 9 Bounded Harmonic Functions -- 10 Entropy -- 11 Compact Group Actions and Boundaries -- 12 Poisson Boundaries -- 13 Hyperbolic Groups -- 14 Unbounded Harmonic Functions -- 15 Groups of Polynomial Growth -- Appendix A: A 57-Minute Course in Measure-Theoretic Probability.
520 $a This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
650 0 $a Random walks (Mathematics) $3 532102
650 0 $a Infinite groups. $3 526101
650 1 4 $a Probability Theory. $3 3538789
650 2 4 $a Potential Theory. $3 893956
650 2 4 $a Group Theory and Generalizations. $3 893889
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 297. $3 3634472
856 4 0 $u https://doi.org/10.1007/978-3-031-25632-5
950 $a Mathematics and Statistics (SpringerNature-11649)