Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Boundary and Entropy of Space Homogeneous Markov Chains

Vadim A. Kaimanovich and Wolfgang Woess
The Annals of Probability
Vol. 30, No. 1 (Jan., 2002), pp. 323-363
Stable URL: http://www.jstor.org/stable/2692012
Page Count: 41
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available

Abstract

We study the Poisson boundary ($\equiv$ representation of bounded harmonic functions) of Markov operators on discrete state spaces that are invariant under the action of a transitive group of permutations. This automorphism group is locally compact, but not necessarily discrete or unimodular. The main technical tool is the entropy theory which we develop along the same lines as in the case of random walks on countable groups, while, however, the implementation is different and exploits discreteness of the state space on the one hand and the path space of the induced random walk on the nondiscrete group on the other. Various new examples are given as applications, including a description of the Poisson boundary for random walks on vertex-transitive graphs with infinitely many ends and on the Diestel-Leader graphs.

• 323
• 324
• 325
• 326
• 327
• 328
• 329
• 330
• 331
• 332
• 333
• 334
• 335
• 336
• 337
• 338
• 339
• 340
• 341
• 342
• 343
• 344
• 345
• 346
• 347
• 348
• 349
• 350
• 351
• 352
• 353
• 354
• 355
• 356
• 357
• 358
• 359
• 360
• 361
• 362
• 363