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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/6/729 |
| Summary: | 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. |
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| ISSN: | 1099-4300 |