TY - JOUR
T1 - A Multi-Layer Extension of the Stochastic Heat Equation
AU - O'Connell, Neil
AU - Warren, Jon
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84952983085&partnerID=8YFLogxK
U2 - 10.1007/s00220-015-2541-3
DO - 10.1007/s00220-015-2541-3
M3 - Article (Academic Journal)
AN - SCOPUS:84952983085
SN - 0010-3616
VL - 341
SP - 1
EP - 33
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -