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 x1

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Author Alexander J Dunlap Mathematics