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With $t_n=32N^2+16N\ln (N+1)$, one obtains: $\P_X(\tau > t_n)\leq \frac{1}{4}$. Therefore, using the definition of $t_{\rm mix}$ and Theorem~\ref{thm-sst}, it follows that -$t_{\rm mix}\leq 32N^2+16N\ln (N+1)=O(N^2)$. +$t_{\rm mix}(\frac{1}{4})\leq 32N^2+16N\ln (N+1)=O(N^2)$ and that + Notice that the calculus of the stationary time upper bound is obtained diff --git a/texput.log b/texput.log index 3eba9c9..1ededd3 100644 --- a/texput.log +++ b/texput.log @@ -1,21 +1,21 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=pdflatex 2016.9.2) 14 OCT 2016 13:12 +This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=pdflatex 2016.11.27) 12 DEC 2016 09:37 entering extended mode restricted \write18 enabled. %&-line parsing enabled. -**sujet.tex +**correctionSeance3.tex presPRNG.tex ! Emergency stop. -<*> sujet.tex - +<*> correctionSeance3.tex + presPRNG.tex End of file on the terminal! 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