A Multi-Layer Extension of the Stochastic Heat Equation

Neil O'Connell, Jon Warren

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)
265 Downloads (Pure)


Motivated by recent developments on solvable directed polymer models, we define a ‘multi-layer’ extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture.

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalCommunications in Mathematical Physics
Issue number1
Early online date24 Dec 2015
Publication statusPublished - 1 Jan 2016


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