Multi-target search in bounded and heterogeneous environments: a lattice random walk perspective
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929649850777600 |
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| author | Giuggioli, Luca Sarvaharman, Seeralan Das, Debraj Marris, Daniel Kay, Toby |
| author_facet | Giuggioli, Luca Sarvaharman, Seeralan Das, Debraj Marris, Daniel Kay, Toby |
| contents | For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations. Recent advances in lattice random walk theory in bounded and heterogeneous environments have opened up opportunities to cope with the finely resolved spatio-temporal nature of modern movement data. We review such advances and their formalisms to represent analytically the walker spatio-temporal dynamics in arbitrary dimensions and geometries. As new findings, we derive the exact spatio-temporal representation of biased walks in a periodic hexagon, we use the discrete Feynman-Kac equation to describe a walker's interaction with a radiation boundary, and we unearth a disorder indifference phenomenon. To demonstrate the power of the formalism we uncover the appearance of multiple first-passage peaks with biased walkers in a periodic hexagon, we display the dependence of the first-transmission probability on the proximity transfer efficiency between two resetting walkers in a one-dimensional periodic lattice, we present an example of spatial disorder in a two-dimensional square lattice that strongly affects the splitting probabilities to either of two targets, and we study the first-reaction dynamics to a single lattice site in an unbounded one-dimensional lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00464 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-target search in bounded and heterogeneous environments: a lattice random walk perspective Giuggioli, Luca Sarvaharman, Seeralan Das, Debraj Marris, Daniel Kay, Toby Statistical Mechanics For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations. Recent advances in lattice random walk theory in bounded and heterogeneous environments have opened up opportunities to cope with the finely resolved spatio-temporal nature of modern movement data. We review such advances and their formalisms to represent analytically the walker spatio-temporal dynamics in arbitrary dimensions and geometries. As new findings, we derive the exact spatio-temporal representation of biased walks in a periodic hexagon, we use the discrete Feynman-Kac equation to describe a walker's interaction with a radiation boundary, and we unearth a disorder indifference phenomenon. To demonstrate the power of the formalism we uncover the appearance of multiple first-passage peaks with biased walkers in a periodic hexagon, we display the dependence of the first-transmission probability on the proximity transfer efficiency between two resetting walkers in a one-dimensional periodic lattice, we present an example of spatial disorder in a two-dimensional square lattice that strongly affects the splitting probabilities to either of two targets, and we study the first-reaction dynamics to a single lattice site in an unbounded one-dimensional lattice. |
| title | Multi-target search in bounded and heterogeneous environments: a lattice random walk perspective |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2311.00464 |