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The Airy sheet: one sample

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The Airy sheet: one sample

av borodin

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One sample of the prelimit Airy sheet S(x,y) on [-1.5,1.5]^2, from exponential last-passage percolation (n = 8000) with both endpoints varying, on a 251 x 251 grid, after KPZ rescaling. Its mean shape is the ridge -(x-y)^2. The texture runs parallel to the axes: geodesics with nearby endpoints share

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One sample of the prelimit Airy sheet S(x,y) on [-1.5,1.5]^2, from exponential last-passage percolation (n = 8000) with both endpoints varying, on a 251 x 251 grid, after KPZ rescaling. Its mean shape is the ridge -(x-y)^2. The texture runs parallel to the axes: geodesics with nearby endpoints share their middle, so locally S(x,y) = f(x) + g(y) (Basu-Ganguly-Hammond).

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