gap.tex

Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
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29 \draw[->,line width=.6pt] (0.8,0.65) -- (0.8,4.02);
30 \node[font=\small,align=center,font=\scriptsize] at (5.1,0.1) {generator perturbation $\varepsilon$};
31 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (0.8,4.3) {square-root difference};
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35 \node[font=\small,align=center,font=\small] at (11.8,3.85) {no gap: $\sqrt{\varepsilon}$};
36 \node[font=\small,align=center,font=\small] at (11.8,2.8) {gap one: $\sqrt{1+\varepsilon}-1$};
37 \node[font=\small,align=center,font=\small] at (11.8,1.75) {certificate: $\varepsilon/2$};
38 \node[font=\small,align=center,font=\scriptsize] at (11.8,0.65) {No uniform linear bound\\can hold at zero.};
39 \end{tikzpicture}

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