Timeline for Reference Request: Simple Random Walk on $\mathbb Z$ is Unimodal
Current License: CC BY-SA 4.0
3 events
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| Jul 25, 2018 at 16:35 | comment | added | Sam OT | I have realised, however, that my question was poorly worded. The reference you've given basically just says that $P_s(x,y) \le P_s(x,x)$ for all $x$ and $y$; this is in Aldous-Fill and Levin-Peres-Wilmer. One then obtains my desired monotonicity by considering $r$ and $r+1$ and using the strong Markov property at the hitting time of $r$. | |
| Jul 25, 2018 at 16:26 | comment | added | Sam OT | Thanks for the reference. The English Google Books preview didn't allow me page 335, but the Dutch one does! | |
| Jul 25, 2018 at 11:40 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |