\begin{center}
    \begin{minipage}{0.4\linewidth}
        \begin{figure}
            \centering
            \begin{minipage}{0.5\linewidth}
                \begin{tikzpicture}[domain=-0.5:2]
                    \draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);

                    \draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
                    \draw[->] (0,-0.7) -- (0,2.2) node[above] {$V(x,\omega)$};

                    \draw (0,0) -- (1,0) plot coordinates {(0,0)  (1,0)}[color=red];
                    \draw (1,1) -- (2,1) plot coordinates {(1,1)  (2,1)}[color=red];
                    \draw (0,0) node[left] {$0$};
                    \draw (0,1) node[left] {$1$};
                    \draw (1,-0.7) node[below] {$\omega_0$};
                \end{tikzpicture}
            \end{minipage}
            \hspace{3mm}
            \begin{minipage}{0.4\linewidth}
                \caption{Visibility of a point $x$ with respect to $\omega$.}
                \label{fig:visibility}
            \end{minipage}
        \end{figure}
    \end{minipage}
    % second diagram
    \begin{minipage}{0.5\linewidth}
        \begin{figure}
            \centering
            \begin{minipage}{0.5\linewidth}
                \begin{tikzpicture}[domain=-0.5:2]
                    \draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);

                    \draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
                    \draw[->] (0,-0.7) -- (0,2.2) node[above] {$\frac{\partial}{\partial\omega}V(x,\omega)$};

                    \draw (0,0) -- (2,0) plot coordinates {(0,0)  (2,0)}[color=red];
                    \draw (0,0) node[left] {$0$};
                    \draw (0,1) node[left] {$1$};
                    \draw (0,2) node[left] {$\infty$};
                    \draw (1,2) node[color=red] {$\bullet$};
                    \draw (1,-0.7) node[below] {$\omega_0$};
                \end{tikzpicture}
            \end{minipage}
            \begin{minipage}{0.4\linewidth}
                \caption{Differentiation of the left graph with respect to $\omega$.}
                \label{fig:dirac-delta-spike}
            \end{minipage}
        \end{figure}
    \end{minipage}
\end{center}