## Aas, Erik and Sjöstrand, Jonas - A product formula for the TASEP on a ring

dmtcs:2429 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
A product formula for the TASEP on a ring

Authors: Aas, Erik and Sjöstrand, Jonas

For a random permutation sampled from the stationary distribution of the TASEP on a ring, we show that, conditioned on the event that the first entries are strictly larger than the last entries, the $\textit{order}$ of the first entries is independent of the $\textit{order}$ of the last entries. The proof uses multi-line queues as defined by Ferrari and Martin, and the theorem has an enumerative combinatorial interpretation in that setting. Finally, we present a conjecture for the case where the small and large entries are not separated.

Source : oai:HAL:hal-01207537v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: random permutation,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]