Abstract
The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of the two systems are nearly uncorrelated for a very long time. One of the consequences of this fact is that a stochastic heat equation with regular coefficients is a finite system if and only if the initial state is integrable.
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Research supported in part by a Swiss Federal Fellowship (L.C.), a Technion Fellowship (K.K), Science Foundation Grant 1131/14 (K.K), an individual investigator grant from the United States’ National Science Foundation (D.K.; DMS-1307470) and a United States National Science Foundation grant through Kavli Institute for Theoretical Physics at UCSB (D.K.; PHY11-25915)
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Chen, L., Khoshnevisan, D. & Kim, K. Decorrelation of Total Mass Via Energy. Potential Anal 45, 157–166 (2016). https://doi.org/10.1007/s11118-016-9540-7
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DOI: https://doi.org/10.1007/s11118-016-9540-7