A multi-layer extension of the stochastic heat equation
The KPZ universality class is expected to contain a large class of random growth processes. In some of these models, there is an additional structure provided by multiple non-intersecting paths and utilisation of this additional structure has led to derivations of exact formulae for the distribution...
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University of Warwick
2016
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| Online Access: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685197 |
| Summary: | The KPZ universality class is expected to contain a large class of random growth processes. In some of these models, there is an additional structure provided by multiple non-intersecting paths and utilisation of this additional structure has led to derivations of exact formulae for the distribution of quantities of interest. Motivated by this we study the multi-layer extension of the stochastic heat equation introduced by O'Connell and Warren in [OW11] which is the continuum analogue of the above mentioned structure. We also show that a multi-layer Cole-Hopf solution to the KPZ equation is well defined. |
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