For identically distributed weights on the lattice, last passage percolation times are maximized in increasing convex order by a coupling that for exponential marginals yields R_N equal to N times one weight plus log(N!).
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Convex bounds for last passage percolation with dependent identically distributed weights
For identically distributed weights on the lattice, last passage percolation times are maximized in increasing convex order by a coupling that for exponential marginals yields R_N equal to N times one weight plus log(N!).