Timeline for Question about the proof of Propp-Wilson algorithm in Olle Häggström's book
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 16, 2023 at 3:30 | comment | added | zemora | Hi, I have edited my question. I guess the ambiguity of $\tilde{Y}$ is not the main problem, because one can define $\tilde{Y}$ by using the last random stream that succeeded in producing a coupling? Isn't the use of old randomness lies in the argument "by the arbitrariness of $\epsilon$"? Because resuing old randomness ensures that once we go further into the past, all chains will still couple at $Y$, hence the left hand of $|P(Y=s_i)-\pi(s_i)|\leq\epsilon$ does not change? | |
| Dec 14, 2023 at 18:59 | history | edited | jlewk | CC BY-SA 4.0 |
typo in states {1,2,3} versus {0,1,2}. Now {0,1,2} is used everywhere.
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| Dec 1, 2023 at 7:43 | comment | added | jlewk | If all previous randomness is thrown away everytime $i$ is increased, how to pick the randomness to define $\tilde Y$? We have now several candidates since the randomness indexed at $-1$ has been resampled $i$ times. By not throwing away, $\tilde Y$ is well defined. | |
| Dec 1, 2023 at 6:57 | comment | added | zemora | Thank you. I know the counterexamples that demonstrate why one should reuse randomness, and why coupling into the future will not work. What puzzled me is how they are used in the proof, because the proof itself did not explicitly say "Since we are using the old randomness, we have blahblah..." | |
| Dec 1, 2023 at 5:44 | history | edited | jlewk | CC BY-SA 4.0 |
Add definition of random f
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| Dec 1, 2023 at 5:31 | history | answered | jlewk | CC BY-SA 4.0 |