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• W3099757028 abstract "We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A<0$. We provide an exact solution, using replica Bethe ansatz methods, to two problems which were recently proved to be equivalent [Parekh, arXiv:1901.09449]: the droplet initial condition for arbitrary $A geqslant -1/2$, and the Brownian initial condition with a drift for $A=+infty$ (infinite hard wall). We study the height at $x=0$ and obtain (i) at all time the Laplace transform of the distribution of its exponential (ii) at infinite time, its exact probability distribution function (PDF). These are expressed in two equivalent forms, either as a Fredholm Pfaffian with a matrix valued kernel, or as a Fredholm determinant with a scalar kernel. For droplet initial conditions and $A> - frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= frac{1}{2}$, the critical point at which the DP binds to the wall, we obtain the GOE Tracy-Widom distribution. In the critical region, $A+frac{1}{2} = epsilon t^{-1/3} to 0$ with fixed $epsilon = mathcal{O}(1)$, we obtain a transition kernel continuously depending on $epsilon$. Our work extends the results obtained previously for $A=+infty$, $A=0$ and $A=- frac{1}{2}$." @default.
• W3099757028 created "2020-11-23" @default.
• W3099757028 creator A5031449563 @default.
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• W3099757028 date "2020-03-04" @default.
• W3099757028 modified "2023-10-16" @default.
• W3099757028 title "Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line" @default.
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• W3099757028 doi "https://doi.org/10.21468/scipostphys.8.3.035" @default.
• W3099757028 hasPublicationYear "2020" @default.
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