Séminaire du LPTMS : Guillaume Barraquand (ENS Paris)


11:00 - 12:00

Type d’évènement

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Stationary measures for the KPZ equation

Guillaume Barraquand (École normale supérieure)

Hybrid: onsite seminar + zoom.

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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.

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