Title: Persistence-like distance on Tamarkin's category and symplectic displacement energy,
Abstract: We introduce a persistence-like pseudo-distance on Tamarkin's category and
prove that the distance between an object and its Hamiltonian deformation is at
most the Hofer norm of the Hamiltonian function. Using the distance, we show a
quantitative version of Tamarkin's non-displaceability theorem, which gives a
lower bound of the displacement energy of compact subsets in a cotangent
bundle.