Random Walks on Infinite Groups
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 sym...
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| Materyal Türü: | Elektronik Ekitap |
| Dil: | İngilizce |
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Cham :
Springer International Publishing : Imprint: Springer,
2023.
|
| Edisyon: | 1st ed. 2023. |
| Seri Bilgileri: | Graduate Texts in Mathematics,
297 |
| Konular: | |
| Online Erişim: | https://doi.org/10.1007/978-3-031-25632-5 |
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| 100 | 1 | |a Lalley, Steven P. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Random Walks on Infinite Groups |h [electronic resource] / |c by Steven P. Lalley. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XII, 369 p. 1 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of colour is Not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
| 341 | 0 | |b Next / Previous structural navigation |2 onix | |
| 341 | 0 | |b All Non-decorative content supports reading without sight |2 onix | |
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| 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Potential theory (Mathematics). | |
| 650 | 0 | |a Group theory. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Potential Theory. |
| 650 | 2 | 4 | |a Group Theory and Generalizations. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031256318 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031256332 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031256349 |
| 830 | 0 | |a Graduate Texts in Mathematics, |x 2197-5612 ; |v 297 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-25632-5 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||