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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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Detalles Bibliográficos
Autor principal: Montero, Miquel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
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.
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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
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