Kannan–Tetali–Vempala conjecture (bipartite/binary-matrix case)

The swap chain flips checkerboard 2×2 blocks to sample 0/1 matrices with fixed row and column sums. Kannan, Tetali and Vempala conjectured in 1997 that it mixes in polynomial time for all feasible margins; the lazy chain is shown to have spectral gap at least $\binom{m}{2}^{-1}\binom{n}{2}^{-1}$ on $m \times n$ matrices, which is worst-case tight and settles the bipartite case.