Potential Analysis

, Volume 45, Issue 1, pp 157–166 | Cite as

Decorrelation of Total Mass Via Energy



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.


The stochastic heat equation Finite particle systems Total mass Mutual energy 

Mathematics Subject Classification (2010)

Primary 60H15 60H25; Secondary 35R60 60K37 60J30 60B15 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  3. 3.Department of Industrial Engineering and ManagementTechnion—Israel Institute of TechnologyHaifaIsrael

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