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Using the structure of the jet schemes of rational double pointsingularities, we construct "minimal embedded toric resolutions" of thesesingularities. We also establish, for these singularities, a correspondencebetween a natural class of irreducible components of the jet schemes centeredat the singular locus and the set of divisors which appear on every "minimalembedded toric resolution". We prove that this correspondence is bijectiveexcept for the $E_8$ singulartiy. This can be thought as an embedded Nashcorrespondence for rational double point singularities.

Jet schemes and minimal toric embedded resolutions of rational double point singularities