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Renormalizing the Kardar-Parisi-Zhang equation in \(d\ge 3\) in weak disorder.(English)Zbl 1434.60278

Summary: We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random limit as the smoothing parameter is turned off. We identify this limit, in the case of general initial conditions ranging from flat to droplet. We provide strong approximations of the solution which obey exactly the limit law. We prove that this limit has sub-Gaussian lower tails, implying existence of all negative (and positive) moments.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
35R60 PDEs with randomness, stochastic partial differential equations
35Q82 PDEs in connection with statistical mechanics
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82D60 Statistical mechanics of polymers

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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