Baik–Corwin–Guaraco–Romik distributional identity for oriented swap and last-passage vectors

Let $\mathbf{U}_N=(U_N(1),\dots,U_N(N-1))$ be the vector of swap-passage times in the oriented swap process, and let $\mathbf{V}_N=(V_N(1),\dots,V_N(N-1))$ be the vector of last-passage times in the corresponding exponential-weight oriented percolation model, for $N\geq 2$. Baik–Corwin–Guaraco–Romik conjecture. The random vectors have the same distribution:

$$\mathbf{U}_N \stackrel{d}{=} \mathbf{V}_N.$$

This identity was conjectured as a hidden symmetry relating the oriented swap process to exponential last-passage percolation. In the paper, it is used to derive the Tracy–Widom asymptotics for the absorbing time; the conjecture itself is therefore resolved by the stated results.