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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8228639/ https://www.ncbi.nlm.nih.gov/pubmed/34201220 http://dx.doi.org/10.3390/e23060729 |
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author | Montero, Miquel |
author_facet | Montero, Miquel |
author_sort | Montero, Miquel |
collection | PubMed |
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. |
format | Online Article Text |
id | pubmed-8228639 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-82286392021-06-26 Random Walks with Invariant Loop Probabilities: Stereographic Random Walks Montero, Miquel Entropy (Basel) Article 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. MDPI 2021-06-08 /pmc/articles/PMC8228639/ /pubmed/34201220 http://dx.doi.org/10.3390/e23060729 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Montero, Miquel Random Walks with Invariant Loop Probabilities: Stereographic Random Walks |
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 | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8228639/ https://www.ncbi.nlm.nih.gov/pubmed/34201220 http://dx.doi.org/10.3390/e23060729 |
work_keys_str_mv | AT monteromiquel randomwalkswithinvariantloopprobabilitiesstereographicrandomwalks |