Phase Transition in Reinforced Random Walk and RWRE on Trees
| Autor: | Robin Pemantle |
|---|---|
| Rok vydání: | 1988 |
| Předmět: |
Statistics and Probability
60J80 Phase transition Markov chain Polya urn Process (computing) Value (computer science) Reinforced random walk Random walk mixture of Markov chains Combinatorics Mathematics::Probability 60J15 random walk on trees Random environment Transient (computer programming) Statistical physics Tree (set theory) Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Ann. Probab. 16, no. 3 (1988), 1229-1241 |
| ISSN: | 0091-1798 |
| Popis: | A random walk on an infinite tree is given a particular kind of positive feedback so edges already traversed are more likely to be traversed in the future. Using exchangeability theory, the process is shown to be equivalent to a random walk in a random environment (RWRE), that is to say, a mixture of Markov chains. Criteria are given to determine whether a RWRE is transient or recurrent. These criteria apply to show that the reinforced random walk can vary from transient to recurrent, depending on the value of an adjustable parameter measuring the strength of the feedback. The value of the parameter at the phase transition is calculated. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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