Timeline for Verifying if Markov process's dependency on time is not random

9 events

when toggle format	what		by	license	comment
S Sep 19, 2017 at 20:26	history	suggested	oxonianftw	CC BY-SA 3.0	made question more straightforward
Sep 19, 2017 at 19:35	review	Suggested edits
S Sep 19, 2017 at 20:26
S Sep 18, 2017 at 21:57	history	suggested	oxonianftw	CC BY-SA 3.0	more explicit
Sep 18, 2017 at 21:44	review	Suggested edits
S Sep 18, 2017 at 21:57
Sep 18, 2017 at 8:18	comment	added	Mateusz Kwaśnicki		@IndoUbt: This is why I wrote "roughly". I do not even claim comparability of $P(k)$ and $(1-2/n^2)^k$ for large $k$. The decay is in fact exponential, of the form $C \lambda^k$, where $\lambda$ is the largest eigenvalue of a killed Markov chain that describes both objects simultaneously (and it is killed when the objects meet). However, I am not sure if this answers the original question.
Sep 18, 2017 at 6:45	comment	added	Indo Ubt		@MateuszKwaśnicki For a 3 row grid, $(1-2/(3)^2)^k$ would give a < 1 value for k < 2. Similarly for all $n\ge3$
Sep 17, 2017 at 22:29	comment	added	Mateusz Kwaśnicki		I bet it will decrease exponentially, roughly as $(1-2/n^2)^k$, where $k$ is the number of steps. This is because after a long period of time, the position of each of the objects becomes almost uniform on black/white squares of the chessboard for even/odd $k$, and roughly independent from whether the objects already met or not.
Sep 17, 2017 at 22:10	review	First posts
Sep 17, 2017 at 23:11
Sep 17, 2017 at 22:05	history	asked	oxonianftw	CC BY-SA 3.0