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Abstract |
A solution h(x,t) of the KPZ equation in one dimension typically grows linearly in time with t^{1/3} fluctuations.
The height gradient, however, or the differences of height between any two points, will reach a stationary
state. In that sense, it has been known for a long time that the Brownian motion is a stationary measure for
the KPZ equation on the full-line. For domains with boundaries such as [0,L] or R_+, stationary measures
were characterized only recently using a combination of works by several groups, and can be described using
Brownian motions reweighted by exponential functionals. The talk is based on joint works with Pierre Le
Doussal and Ivan Corwin. |
