Timeline for Randomly walking a leashed dog
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2014 at 16:14 | comment | added | Joseph O'Rourke | @NateEldredge: The human moves $\pm 1$ in any direction. Then the dog moves $\pm 1$ in any direction that satisfies the leash length constraint. | |
| Mar 1, 2014 at 16:09 | comment | added | Nate Eldredge | Incidentally, it might also be interesting to see what happens if the dog can move faster than the human (a realistic assumption, in my experience). | |
| Mar 1, 2014 at 16:07 | comment | added | Nate Eldredge | I'm not sure I completely understand the model. Is the idea that the human chooses which direction to move, and then the dog chooses uniformly from those directions available to him, given the constraint of the leash? Another interpretation would be that the human and dog move independently, but then we condition them to stay close. | |
| Mar 1, 2014 at 13:15 | vote | accept | Joseph O'Rourke | ||
| Mar 1, 2014 at 7:58 | comment | added | j.c. | This problem seems very much related to the previous question on the inchworm. Thus I think the process described here also should fit in the formalism of a "random walk with internal degrees of freedom"; see mathoverflow.net/a/132218 | |
| Mar 1, 2014 at 5:16 | answer | added | Evan Jenkins | timeline score: 17 | |
| Mar 1, 2014 at 3:56 | answer | added | John Pardon | timeline score: 6 | |
| Mar 1, 2014 at 3:34 | comment | added | The Masked Avenger | Here is something which may also be of interest, on which I have no intuition. Consider that the human faces a particular direction, and then walks that direction. Consider the relative position of the dog after the step is taken and using the orientation of the human. This distribution might be biased in favor of positions away from the direction faced by the human | |
| Mar 1, 2014 at 3:23 | comment | added | Joseph O'Rourke | @TheMaskedAvenger: That's what the histogram shows---relative distance of dog to human. Oh, I see what you mean! I'll compute that eventually... | |
| Mar 1, 2014 at 3:21 | comment | added | The Masked Avenger | In particular, I think you are taking too short a walk. I intuit (perhaps wrongly) that for a leash of length l, walks of length larger than l^2 log l will have the ball distribution start to bunch up at the longer lengths. Try simulations with both really long walks as well as really short leashes. | |
| Mar 1, 2014 at 3:10 | comment | added | The Masked Avenger | Note that the freedom to increase or maintain distance is curtailed only by when the rope is taut. The freedom to decrease or maintain distance is determined by relative position. A distribution of relative positions inside the ball around the human is likely to be more informative. | |
| Mar 1, 2014 at 2:54 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |