RP is the class of problems decidable by a nondeterministic Turing machine that terminates in polynomial time, but that is also allowed one-sided error. P is the usual class of problems decidable by a deterministic Turing machine that terminates in polynomial time.
P = RP follows from a relationship in circuit complexity. Impagliazzo and Wigderson showed that P = BPP follows if some problem that can be decided in deterministic exponential time also requires exponential size circuits (note that P = BPP implies P = RP). Perhaps due to these results, there seems to be a feeling among some complexity theorists that probabilistic reductions can probably be derandomized.
What other specific evidence is there that P = RP?