The completeness of the Bethe ansatz for the periodic ASEP. arXiv:1511.03762
Preprint, arXiv:1511.03762 [math-ph] (2015).
Summary: 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.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
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