Random walks and Brownian motion on cubical complexes
| Autor: | Tom M. W. Nye |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Pure mathematics Distribution (number theory) Applied Mathematics 010102 general mathematics Context (language use) Random walk 01 natural sciences 010104 statistics & probability Metric space Mathematics::Probability Unit cube Modeling and Simulation Tree (set theory) 0101 mathematics Cube Brownian motion Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 130:2185-2199 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2019.06.013 |
| Popis: | Cubical complexes are metric spaces constructed by gluing together unit cubes in an analogous way to the construction of simplicial complexes. We construct Brownian motion on such spaces, define random walks, and prove that the transition kernels of the random walks converge to that for Brownian motion. The proof involves pulling back onto the complex the distribution of Brownian sample paths on a single cube, combined with a distribution on walks between cubes. The main application lies in analysing sets of evolutionary trees: several tree spaces are cubical complexes and we briefly describe our results and applications in this context. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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