Timeline for Spiral lattice random walk
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2017 at 11:56 | vote | accept | Joseph O'Rourke | ||
| Jun 24, 2017 at 12:37 | answer | added | Joseph O'Rourke | timeline score: 5 | |
| Jun 23, 2017 at 23:00 | answer | added | Serguei Popov | timeline score: 7 | |
| Jun 23, 2017 at 22:05 | answer | added | Gerhard Paseman | timeline score: 2 | |
| Jun 23, 2017 at 21:52 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 168 characters in body
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| Jun 23, 2017 at 20:47 | comment | added | Martin Hairer | The scaling limit of the norm seems to be a Bessel 3 process, so it should be transient... | |
| Jun 23, 2017 at 20:37 | comment | added | Anthony Quas | I believe the answer is that this is recurrent. If you let $R_n=|X_n|$, this has the same kind of decaying drift to $+\infty$ as the standard 2D Brownian motion: $R_{n+1}\approx R_n + c/\sqrt{R_n}$. | |
| Jun 23, 2017 at 14:49 | comment | added | Ori Gurel-Gurevich | I'm not immediately sure what the answer is, but I think the spiral thing is a bit of a red herring. What you should look at is does this random walk give the same parameter for the corresponding Bessel process. For d dimensional BM the parameter is $\frac{d-1}{2}$ and $\frac12$ is the critical parameter for recurrence, corresponding to $d=2$. I don't have time right now to calculate the parameter for the spiral RW. | |
| Jun 23, 2017 at 13:07 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |