Random Walks with Invariant Loop Probabilities: Stereographic Random Walks

Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying ge...

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Veröffentlicht in:Entropy (Basel, Switzerland) Switzerland), 2021-06, Vol.23 (6), p.729
1. Verfasser: Montero, Miquel
Format: Artikel
Sprache:eng
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Zusammenfassung:Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23060729