Correction: Stationary Solutions to the Stochastic Burgers Equation on the Line (Communications in Mathematical Physics, (2021), 382, 2, (875-949), 10.1007/s00220-021-04025-x)

The first identity in (5.6) of the referenced article is incorrect: the correct version would have E^X0,00,tE^X~0,00,t on the right side rather than E^X0,00,qE^X~0,00,q, but with this change the rest of the proof does not go through. Therefore, we retract the statement in Proposition 5.2 that γ is concave. This claim is used in two places in the article, and both can be replaced with other arguments, so all of the main results still hold. First, the statement of Lemma 5.4 should be replaced with the following: Suppose that a∈R and u is a solution to (1.3) with initial condition u(0,·)≡a. Then for all t>q≥0 and x∈R, we have (Formula presented.) The proof is unchanged through equation (5.7). But then, instead of using the claim in question that γ is concave, we simply use Lemma 5.3 and (5.7) in (5.6) to obtain (Formula presented.) and then conclude the statement of the lemma since this holds for all x10. By Proposition 2.2 and the discussion following it, we see that there is an Mε<∞ such that, for any t≥2 and any s∈[t-2,t-1], we have (Formula presented.) Also by Proposition 2.2 and the discussion following it, we see that for every ε>0, there is a compact set Kε⊂X1/2 such that for any t≥2, we have (Formula presented.) Moreover, by (0.1), for any t≥2 we have some s∈[t-2,t-1] such that E‖u(s,·)‖Cw~(R)2≤C, which means by Markov’s inequality that (Formula presented.) Combining (0.2), (0.3), and (0.4), we see that for any t≥2 we have (Formula presented.) which completes the proof of tightness. Finally, in the proof of Proposition 7.5, the phrase “uniformly bounded” before (7.13) should be replaced by “locally integrable.” The authors are grateful to Yu Gu for pointing out the error.