Trickle-down processes and their boundaries
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Trickle-down processes and their boundaries |
| 2. | Creator | Author's name, affiliation, country | Steven Neil Evans; University of California at Berkeley; United States |
| 2. | Creator | Author's name, affiliation, country | Rudolf Grübel; Leibniz Universität Hannover; Germany |
| 2. | Creator | Author's name, affiliation, country | Anton Wakolbinger; Goethe-Universität Frankfurt am Main; Germany |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | harmonic function; h-transform; tail sigma-field; diffusion limited aggregation; search tree; Dirichlet random measure; random recursive tree; Chinese restaurant process; Ewens sampling formula; GEM distribution; Mallows model; q-binomial; Catalan |
| 3. | Subject | Subject classification | 60J50; 60J10; 68W40 |
| 4. | Description | Abstract | It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-by-one at a distinguished source vertex, successive particles proceed along directed edges according to an appropriate stochastic mechanism, and each particle comes to rest once it encounters an unoccupied vertex. Examples include the binary and digital search tree processes, the random recursive tree process and generalizations of it arising from nested instances of Pitman's two-parameter Chinese restaurant process, tree-growth models associated with Mallows' $\phi$ model of random permutations and with Schützenberger's non-commutative $q$-binomial theorem, and a construction due to Luczak and Winkler that grows uniform random binary trees in a Markovian manner. We introduce a framework that encompasses such Markov chains, and we characterize their asymptotic behavior by analyzing in detail their Doob-Martin compactifications, Poisson boundaries and tail $\sigma$-fields. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | National Science Foundation grants DMS-0405778 and DMS-0907630 |
| 7. | Date | (YYYY-MM-DD) | 2012-01-01 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ejp.ejpecp.org/article/view/1698 |
| 10. | Identifier | Digital Object Identifier | 10.1214/EJP.v17-1698 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 17 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
| 15. | Rights | Copyright and permissions | The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free
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