Infinite cycles in the interchange process in five dimensions (Elboim-Sly), formalized in Lean 4
Source: github.com/scottnarmstrong/elboim-sly/tree/3191c5f9c55c0662…
A complete Lean 4 formalization of D. Elboim and A. Sly, Infinite cycles in the interchange process in five dimensions (arXiv:2211.17023v3). In the interchange process on Z^d, each edge carries an independent rate-one Poisson clock and swaps the particles at its endpoints when it rings; run for time beta, it yields a random permutation pi_beta of Z^d. Toth conjectured that pi_beta has infinite cycles for d >= 3 and beta large; Elboim and Sly proved this for d >= 5. The library proves their Theorem 1 (for d >= 5 and beta large, pi_beta almost surely has an infinite cycle), the quantitative…
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