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In this paper, we study various asymptotic behavior of the infinite family ofmonotone Lagrangian tori $T_{a,b,c}$ in $\mathbb{CP}^2$ associated to Markovtriples $(a,b,c)$ described in \cite{Vi14}. We first prove that the Gromovcapacity of the complement $\mathbb{CP}^2 \setminus T_{a,b,c}$ is greater thanor equal to $\frac13$ of the area of the complex line for all Markov triple$(a,b,c)$. We then prove that there is a representative of the family$\{T_{a,b,c}\}$ whose loci completely miss a metric ball of nonzero size and inparticular the loci of the union of the family is not dense in $\mathbb{CP}^2$.

Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a,b,c}$ in $\mathbb{CP}^2$ as $a+b+c \to \infty$