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Hamiltonian F-stability of complete Lagrangian self-shrinkers

In this paper, we study the Lagrangian F-stability and Hamiltonian F-stability of Lagrangian self-shrinkers. We prove a characterization theorem for the Hamiltonian F-stability of $n$-dimensional complete Lagrangian self-shrinkers without boundary, with polynomial volume growth and with the second fundamental form satisfying the condition that there exist constants $C_0>0$ and $\varepsilon<\frac{1}{16n}$ such that $|A|^2\leq C_0+\varepsilon |x|^2$. We characterize the Hamiltonian F-stablity by the eigenvalues and eigenspaces of the drifted Laplacian.