https://github.com/jlumbroso/reluctant-walks
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. (Lumbroso, Mishna, Ponty, 2017)
https://github.com/jlumbroso/reluctant-walks
analytic-combinatorics combinatorics random-generation random-walk
Last synced: 4 months ago
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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. (Lumbroso, Mishna, Ponty, 2017)
- Host: GitHub
- URL: https://github.com/jlumbroso/reluctant-walks
- Owner: jlumbroso
- License: lgpl-3.0
- Created: 2018-03-20T21:37:12.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2018-04-03T15:21:11.000Z (over 7 years ago)
- Last Synced: 2025-05-30T12:16:06.433Z (5 months ago)
- Topics: analytic-combinatorics, combinatorics, random-generation, random-walk
- Language: Python
- Homepage:
- Size: 2.33 MB
- Stars: 8
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Sampling from Reluctant Quarter-Plane Walks
Reluctant walks tend to exit the quarter-plane in which they are constrained, but this work shows how to randomly sample large reluctant walks anyway.
## Installation
Since the package is registered in Python's central repository, you can install it using `pip`:
```
pip install reluctant_walks
```
Although the package will degrade gracefully, it has some dependencies for certain of its functionalities:
- The [Sage environment](http://www.sagemath.org/), to solve the equation necessary to compute the best slope for any family of quarter-plane walk. (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.)
- 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.
In 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.
## Example
Below 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.
## Bibliography
Bousquet-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.
Lumbroso, 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.