Probability on trees and networks:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Cambridge University Press
2016
|
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
42 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xv, 699 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107160156 |
Internformat
MARC
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| 100 | 1 | |a Lyons, Russell |e Verfasser |0 (DE-588)1130806618 |4 aut | |
| 245 | 1 | 0 | |a Probability on trees and networks |c Russell Lyons (Indiana University, Bloomington), Yuval Peres (Microsoft Research, Redmond, Washington) |
| 264 | 1 | |a New York |b Cambridge University Press |c 2016 | |
| 300 | |a xv, 699 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics |v 42 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Trees (Graph theory) | |
| 650 | 4 | |a Stochastic processes | |
| 700 | 1 | |a Peres, Yuval |e Verfasser |0 (DE-588)121404420 |4 aut | |
| 830 | 0 | |a Cambridge series in statistical and probabilistic mathematics |v 42 |w (DE-604)BV011442366 |9 42 | |
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Datensatz im Suchindex
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| adam_text | vii Contents Preface Chapter 1: Some Highlights 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Graph Terminology Branching Number Electric Current Random Walks Percolation Branching Processes Random Spanning Trees Hausdorff Dimension Capacity Embedding Trees into Euclidean Space Notes Collected In-Text Exercises Additional Exercises Chapter 2: Random Walks and Electric Networks 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Circuit Basics and Harmonic Functions More Probabilistic Interpretations Network Reduction Energy Transience and Recurrence Rough Isometries and Hyperbolic Graphs Hitting, Commute, and Cover Times The Canonical Gaussian Field Notes Collected In-Text Exercises Additional Exercises xiii 1 1 2 5 6 7 8 9 12 13 15 16 17 17 18 18 24 27 31 36 43 48 50 53 57 59
viii Contents Chapter 3: Special Networks 1. 2. 3. 4. 5. 6. 7. Flows, Cutsets, and Random Paths Trees Growth of Trees Cayley Graphs Notes Collected In-Text Exercises Additional Exercises Chapter 4: Uniform Spanning Trees 1. 2. 3. 4. 5. 6. Generating Uniform Spanning Trees Electrical Interpretations The Square Lattice 1? Notes Collected In-Text Exercises Additional Exercises Chapter 5: Branching Processes, Second Moments, and Percolation 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Galton-Watson Branching Processes The First-Moment Method The Weighted Second-Moment Method Quasi-independent Percolation Transience of Percolation Clusters in ΈΓ Reversing the Second-Moment Inequality Surviving Galton-Watson Trees Harris’s Inequality Galton-Watson Networks Notes Collected In-Text Exercises Additional Exercises Chapter 6: Isoperimetric Inequalities 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Flows and Submodularity Spectral Radius Nonbacktracking Paths and Cogrowth Relative Mixing Rate, Spectral Gap, and Expansion in Finite Networks Planar Graphs Euclidean Lattices and Entropy Expansion Profiles and Decay of Transition Probabilities Anchored Isoperimetric Profiles and Transience Anchored Expansion and Percolation Notes Collected In-Text Exercises Additional Exercises 74 74 79 81 86 90 91 92 95 95 105 Ill 116 123 125 131 132 137 140 143 146 149 153 160 162 164 166 167 174 174 181 186 190 195 200 205 211 213 222 224 225
Contents Chapter 7: Percolation on Transitive Graphs 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. ix 233 Groups and Amenability Tolerance and Ergodicity The Number of Infinite Clusters Inequalities for pc Merging Infinite Clusters and Invasion Percolation Upper Bounds for pu Lower Bounds for pü Bootstrap Percolation on Regular Trees Notes Collected In-Text Exercises Additional Exercises 235 237 240 244 250 255 257 262 264 268 269 Chapter 8: The Mass-Transport Technique and Percolation 273 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. The Mass-Transport Principle for Cayley Graphs Beyond Cayley Graphs: Unimodularity Infinite Clusters in Invariant Percolation Critical Percolation on Nonamenable Transitive Unimodular Graphs Bernoulli Percolation on Planar Quasi-transitive Graphs Properties of Infinite Clusters Invariant Percolation on Amenable Graphs Appendix: Unimodularity of Planar Quasi-transitive Graphs Notes Collected In-Text Exercises Additional Exercises Chapter 9: Infinite Electrical Networks and Dirichlet Functions 1. 2. 3. 4. 5. 6. 7. 8. Free and Wired Electrical Currents Planar Duality Harmonic Dirichlet Functions Planar Graphs and Hyperbolic Graphs Random Walk Traces Notes Collected In-Text Exercises Additional Exercises Chapter 10: Uniform Spanning Forests 1. 2. 3. 4. 5. 6. 7. Limits over Exhaustions Coupling, Harmonic Dirichlet Functions, and Expected Degree Planar Networks and Euclidean Lattices Tail Triviality The Number of Trees The Size of the Trees Loop-Erased Random Walk and Harmonic Measure from Infinity 273 276 282 286 287 291 293 296 299 303 304 309 309 311 313 320 326 330
334 335 339 339 343 350 352 355 364 375
Contents x 8. 9. 10. 11. Appendix: Von Neumann Dimension and i2-Betti Numbers Notes Collected In-Text Exercises Additional Exercises Chapter 11: Minimal Spanning Forests 1. 2. 3. 4. 5. 6. 7. 8. 9. Minimal Spanning Trees Deterministic Results Basic Probabilistic Results Tree Sizes Planar Graphs Nontreeable Groups Notes Collected In-Text Exercises Additional Exercises Chapter 12: Limit Theorems for Galton-Watson Processes 1. 2. 3. 4. 5. 6. 7. Size-Biased Trees and Immigration Supercritical Processes: Proof of the Kesten-Stigum Theorem Subcriticai Processes Critical Processes Notes Collected In-Text Exercises Additional Exercises Chapter 13: Escape Rate of Random Walks and Embeddings 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Basic Examples The Varopoulos-Carne Bound An Application to Mixing Time Markov Type of Metric Spaces Embeddings of Finite Metric Spaces A Diffusive Lower Bound for Cayley Graphs Branching Number of a Graph Tree-Indexed Random Walks Notes Collected In-Text Exercises Additional Exercises 377 382 383 385 388 388 391 395 397 403 404 405 407 408 410 410 414 416 417 420 420 421 423 423 429 431 436 440 447 450 453 456 461 462
Contents Chapter 14: Random Walks on Groups and Poisson Boundaries 1. 2. 3. 4. 5. 6. 7. 8. 9. Tail, Entropy, and Speed for Transitive Markov Chains Harmonic Functions and the Liouville Property Harmonic Functions and the Poisson Boundary Identifying the Poisson Boundary Appendix: Ergodic Theorems Appendix: The Zero-Two Law for Transitive Markov Chains Notes Collected In-Text Exercises Additional Exercises Chapter 15: Hausdorff Dimension 1. 2. 3. 4. 5. 6. 7. 8. Basics Coding by Trees Galton-Watson Fractals Holder Exponent Derived Trees Notes Collected In-Text Exercises Additional Exercises Chapter 16: Capacity and Stochastic Processes 1. 2. 3. 4. 5. 6. 7. 8. Definitions Percolation on Trees Euclidean Space Fractal Percolation and Brownian Intersections Generalized Diameters and Average Meeting Height on Trees Notes Collected In-Text Exercises Additional Exercises Chapter 17: Random Walks on Galton-Watson Trees 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Markov Chains and Ergodic Theory Stationary Measures on Trees Speed on Galton-Watson Trees Harmonic Measure: The Goal Flow Rules and Markov Chains on the Space of Trees The Holder Exponent of Limit Uniform Measure Dimension Drop for Other Flow Rules Harmonic-Stationary Measure Confinement of Simple Random Walk Numerical Calculations Notes Collected In-Text Exercises xi 467 468 474 480 486 494 499 503 508 509 512 512 516 521 524 526 530 530 531 534 534 537 538 541 548 550 553 554 556 556 559 565 569 570 573 576 577 580 583 588 589
xii 13. Additional Exercises Contents 590 Comments on Exercises 594 Bibliography 648 Glossary of Notation 687 Index 690
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| id | DE-604.BV043873696 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:37:21Z |
| institution | BVB |
| isbn | 9781107160156 |
| language | English |
| lccn | 016021811 |
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| physical | xv, 699 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press |
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| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Lyons, Russell Verfasser (DE-588)1130806618 aut Probability on trees and networks Russell Lyons (Indiana University, Bloomington), Yuval Peres (Microsoft Research, Redmond, Washington) New York Cambridge University Press 2016 xv, 699 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics 42 Includes bibliographical references and index Trees (Graph theory) Stochastic processes Peres, Yuval Verfasser (DE-588)121404420 aut Cambridge series in statistical and probabilistic mathematics 42 (DE-604)BV011442366 42 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029283506&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lyons, Russell Peres, Yuval Probability on trees and networks Cambridge series in statistical and probabilistic mathematics Trees (Graph theory) Stochastic processes |
| title | Probability on trees and networks |
| title_auth | Probability on trees and networks |
| title_exact_search | Probability on trees and networks |
| title_full | Probability on trees and networks Russell Lyons (Indiana University, Bloomington), Yuval Peres (Microsoft Research, Redmond, Washington) |
| title_fullStr | Probability on trees and networks Russell Lyons (Indiana University, Bloomington), Yuval Peres (Microsoft Research, Redmond, Washington) |
| title_full_unstemmed | Probability on trees and networks Russell Lyons (Indiana University, Bloomington), Yuval Peres (Microsoft Research, Redmond, Washington) |
| title_short | Probability on trees and networks |
| title_sort | probability on trees and networks |
| topic | Trees (Graph theory) Stochastic processes |
| topic_facet | Trees (Graph theory) Stochastic processes |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029283506&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
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