{"id":22173491,"url":"https://github.com/jlumbroso/reluctant-walks","last_synced_at":"2025-06-17T12:33:02.593Z","repository":{"id":57461107,"uuid":"126085599","full_name":"jlumbroso/reluctant-walks","owner":"jlumbroso","description":"Reluctant walks tend to exit the quarter-plane in which they are constrained (because of strong negative drift), but this work shows how to randomly sample large reluctant walks anyway. 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(Without Sage, it is possible to experiment on the \"*79 non-trivial small stepset models*\" for which we have precomputed the best slope with some accuracy.)\n\n- Either [GenRGenS](https://www.lri.fr/genrgens/index.php?idpage=2) or [Maple](https://www.maplesoft.com/) as a backend to randomly sample walks given an algebraic grammar, if you wish to be able to randomly generate walks.\n\nIn addition, it is recommended to have `matplotlib` to visualize the walks, and Jupyter Notebook to experiment with the package. See the `notebook` folder for examples.\n\n## Example\n\nBelow is a single walk of size 2000 in green, on a backdrop of many other walks that were also sampled, but which do not remain in the upper-right quarter-plane. There are further such examples in the [VisualizingWalks.ipynb](examples/notebooks/VisualizingWalks.ipynb) notebook.\n\n![Plot of a constrained walk in green, on a backdrop of unconstrained walks.](examples/images/example.png?raw=true \"Plot of a constrained walk in green, on a backdrop of unconstrained walks.\")\n\n## Bibliography\n\nBousquet-Mélou, Mireille, and Marni Mishna (2010). \"[Walks with small steps in the quarter plane.](https://arxiv.org/abs/0810.4387)\" *Contemporary Mathematics*, 520, pp. 1-40.\n\nLumbroso, Jeremie, Marni Mishna, and Yann Ponty (2017). \"[Taming Reluctant Random Walks in the Positive Quadrant.](https://www.sciencedirect.com/science/article/pii/S1571065317300793)\" *Electronic Notes in Discrete Mathematics* (59), pp. 99-114.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjlumbroso%2Freluctant-walks","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjlumbroso%2Freluctant-walks","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjlumbroso%2Freluctant-walks/lists"}