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Article

Random Walks with Invariant Loop Probabilities: Stereographic Random Walks

1
Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, Spain
2
Universitat de Barcelona Institute of Complex Systems (UBICS), Martí i Franquès 1, E-08028 Barcelona, Spain
Academic Editor: Eli Barkai
Entropy 2021, 23(6), 729; https://doi.org/10.3390/e23060729
Received: 11 May 2021 / Revised: 1 June 2021 / Accepted: 3 June 2021 / Published: 8 June 2021
(This article belongs to the Special Issue New Trends in 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 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. View Full-Text
Keywords: random walk; heterogeneous medium; survival analysis; hyperbolic geometry; elliptic geometry random walk; heterogeneous medium; survival analysis; hyperbolic geometry; elliptic geometry
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MDPI and ACS Style

Montero, M. Random Walks with Invariant Loop Probabilities: Stereographic Random Walks. Entropy 2021, 23, 729. https://doi.org/10.3390/e23060729

AMA Style

Montero M. Random Walks with Invariant Loop Probabilities: Stereographic Random Walks. Entropy. 2021; 23(6):729. https://doi.org/10.3390/e23060729

Chicago/Turabian Style

Montero, Miquel. 2021. "Random Walks with Invariant Loop Probabilities: Stereographic Random Walks" Entropy 23, no. 6: 729. https://doi.org/10.3390/e23060729

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