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We consider the spectral structure of the Neumann--Poincar\'e operatorsdefined on the boundaries of thin domains of rectangle shape in two dimensions.We prove that as the aspect ratio of the domains tends to $\infty$, orequivalently, as the domains get thinner, the spectra of theNeumann--Poincar\'e operators are densely distributed in the interval$[-1/2,1/2]$.

Spectral structure of the Neumann--Poincar\'e operator on thin domains in two dimensions