The completeness of the Bethe ansatz for the periodic ASEP

Understand

The asymmetric simple exclusion process (ASEP) for N particles on a ring with L sites may be analyzed using the Bethe ansatz.

• In this paper, we provide a rigorous proof that the Bethe ansatz is complete for the periodic ASEP.
• More precisely, we show that for all but finitely many values of the hopping rate, the solutions of the Bethe ansatz equations do indeed yield all L choose N eigenstates.
• The proof follows ideas of Langlands and Saint-Aubin, which draw upon a range of techniques from algebraic geometry, topology and enumerative combinatorics.