Constructs an almost sure bijection from sequences of independent Brownian motions to the directed landscape on the half-plane, with explicit inverse yielding convergence of Brownian last-passage percolation, and applies it to reconstruct the landscape from the parabolic Airy line ensemble.
Since π is an optimizer we also have that Bθ r( x, t ; L) = Bθ r( π ( s) , s ; L) + L( π ( s) , s ; y, t )
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The directed landscape from Brownian motion
Constructs an almost sure bijection from sequences of independent Brownian motions to the directed landscape on the half-plane, with explicit inverse yielding convergence of Brownian last-passage percolation, and applies it to reconstruct the landscape from the parabolic Airy line ensemble.