Montero M. Random Walks with Invariant Loop Probabilities: Stereographic Random Walks.
ENTROPY 2021;
23:e23060729. [PMID:
34201220 PMCID:
PMC8228639 DOI:
10.3390/e23060729]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Revised: 06/01/2021] [Accepted: 06/03/2021] [Indexed: 11/21/2022]
Abstract
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.
Collapse