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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Bibliographic Details
Main Author:	Lun, Chin Hang
Published:	University of Warwick 2016
Subjects:	515 QA Mathematics
Online Access:	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685197

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spelling	ndltd-bl.uk-oai-ethos.bl.uk-6851972017-08-30T03:15:05ZA multi-layer extension of the stochastic heat equationLun, Chin Hang2016The 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.515QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685197http://wrap.warwick.ac.uk/78989/Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	515 QA Mathematics
spellingShingle	515 QA Mathematics Lun, Chin Hang A multi-layer extension of the stochastic heat equation
description	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.
author	Lun, Chin Hang
author_facet	Lun, Chin Hang
author_sort	Lun, Chin Hang
title	A multi-layer extension of the stochastic heat equation
title_short	A multi-layer extension of the stochastic heat equation
title_full	A multi-layer extension of the stochastic heat equation
title_fullStr	A multi-layer extension of the stochastic heat equation
title_full_unstemmed	A multi-layer extension of the stochastic heat equation
title_sort	multi-layer extension of the stochastic heat equation
publisher	University of Warwick
publishDate	2016
url	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685197
work_keys_str_mv	AT lunchinhang amultilayerextensionofthestochasticheatequation AT lunchinhang multilayerextensionofthestochasticheatequation
_version_	1718521165978271744

A multi-layer extension of the stochastic heat equation

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