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# Ran Tao : Fluctuations of half-space KPZ: from 1/2 to 1/3

We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. We then establish optimal fluctuation exponents for the height function in both the subcritical and critical regimes, along with corresponding estimates for the polymer endpoint. Based on a joint work with Yu Gu.

**Category**: Probability**Duration**: 01:00:13**Date**: October 3, 2024 at 3:10 PM**Views**: 0-
**Tags:**seminar, Probability Seminar

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