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We study the entanglement spectrum of a translationally-invariant latticesystem under a random partition, implemented by choosing each site to be in onesubsystem with probability $p\in[0, 1]$. We apply this random partitioning to atranslationally-invariant (i.e., clean) topological state, and argue on generalgrounds that the corresponding entanglement spectrum captures the universalbehavior about its disorder-driven transition to a trivial localized phase.Specifically, as a function of the partitioning probability $p$, theentanglement Hamiltonian $H_{A}$ must go through a topological phase transitiondriven by the percolation of a random network of edge-states. As an example, weanalytically derive the entanglement Hamiltonian for a one-dimensionaltopological superconductor under a random partition, and demonstrate that itsphase diagram includes transitions between Griffiths phases.

Entanglement Spectrum of a Random Partition: Connection with the Localization Transition