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We introduce a persistence-like pseudo-distance on Tamarkin's category andprove that the distance between an object and its Hamiltonian deformation is atmost the Hofer norm of the Hamiltonian function. Using the distance, we show aquantitative version of Tamarkin's non-displaceability theorem, which gives alower bound of the displacement energy of compact subsets of cotangent bundles.

Persistence-like distance on Tamarkin's category and symplectic displacement energy