Timeline for The Angel and Devil problem with a random angel
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2022 at 0:55 | comment | added | RavenclawPrefect | Even $r=1$ should work for positive probability of escape: let the maximum pointwise probability of the (weakened) angel's location at a specific coordinate (given the devil's moves so far, which only decrease it) be $p_n<1$. Then the statement that $\sum_{i=1}^\infty p_i<\infty$, shown in this answer, is equivalent to $\prod_{i=1}^\infty (1-p_i)>0$, i.e. the devil has nonzero odds of all their moves failing. (Since we're conditioning on each failure, the probabilities at each step are independent.) | |
| Mar 15, 2021 at 20:55 | comment | added | JoshuaZ | I've added a bounty. I'll award it to anyone who either solves d=4 or anyone who can get the details of your d=3 to work. | |
| Mar 15, 2021 at 20:50 | comment | added | Will Sawin | @JoshuaZ Indeed - in the comments, I sketch a possible approach to $d=3$. I suspect $d=4$ is the trickiest. | |
| Mar 15, 2021 at 20:44 | comment | added | JoshuaZ | So this leaves just dimensions 3 and 4 open. | |
| Apr 14, 2020 at 12:14 | history | answered | Will Sawin | CC BY-SA 4.0 |