O’Connell, Neil and Warren, Jon (2016) A multi-layer extension of the stochastic heat equation. Communications in Mathematical Physics, 341 (1). pp. 1-33. doi:10.1007/s00220-015-2541-3 ISSN 0010-3616.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Heat equation
Journal or Publication Title:	Communications in Mathematical Physics
Publisher:	Springer
ISSN:	0010-3616
Official Date:	January 2016
Dates:	Date Event January 2016 Published 24 December 2015 Available 22 September 2015 Accepted 26 October 2011 Submitted
Volume:	341
Number:	1
Number of Pages:	33
Page Range:	pp. 1-33
DOI:	10.1007/s00220-015-2541-3
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/I014829/1 (EPSRC)

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