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 |
| _version_ | 1827690301586669568 |
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| author | Miquel Montero |
| author_facet | Miquel Montero |
| author_sort | Miquel Montero |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T10:36:21Z |
| format | Article |
| id | doaj.art-af576f6e8fdc47fa8cf108d707d06b2a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T10:36:21Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-af576f6e8fdc47fa8cf108d707d06b2a2023-11-21T23:15:42ZengMDPI AGEntropy1099-43002021-06-0123672910.3390/e23060729Random Walks with Invariant Loop Probabilities: Stereographic Random WalksMiquel Montero0Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, SpainRandom 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.https://www.mdpi.com/1099-4300/23/6/729random walkheterogeneous mediumsurvival analysishyperbolic geometryelliptic geometry |
| spellingShingle | Miquel Montero Random Walks with Invariant Loop Probabilities: Stereographic Random Walks Entropy random walk heterogeneous medium survival analysis hyperbolic geometry elliptic geometry |
| title | Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
| title_full | Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
| title_fullStr | Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
| title_full_unstemmed | Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
| title_short | Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
| title_sort | random walks with invariant loop probabilities stereographic random walks |
| topic | random walk heterogeneous medium survival analysis hyperbolic geometry elliptic geometry |
| url | https://www.mdpi.com/1099-4300/23/6/729 |
| work_keys_str_mv | AT miquelmontero randomwalkswithinvariantloopprobabilitiesstereographicrandomwalks |