# A product formula for the TASEP on a ring

Abstract : 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.
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Cited literature [9 references]

https://hal.inria.fr/hal-01207537
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• HAL Id : hal-01207537, version 1

### Citation

Erik Aas, Jonas Sjöstrand. A product formula for the TASEP on a ring. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.633-642. ⟨hal-01207537⟩

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