TASEP Exit Times

Jérôme Dorignac; Fred Geniet; Estelle Pitard

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arXiv · 2310.08477

TASEP Exit Times

Jérôme Dorignac·Fred Geniet·Estelle Pitard

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Abstract

We address the question of the time needed by $N$ particles, initially located on the first sites of a finite 1D lattice of size $L$, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when $N \ll L$, the mean exit time of the particles is asymptotically given by $T_N(L) \sim L+β_N \sqrt{L}$ for large lattices. Building upon exact results obtained for 2 particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients $β_N$. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of $N$ particles in the regime where $N$ is finite while the lattice size $L\rightarrow \infty$. This complements previous asymptotic results obtained by Johansson in \cite{Johansson2000} in the limit where both $N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite.

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BibTeX RIS

Jérôme Dorignac, Fred Geniet, Estelle Pitard. 2023-10-12. TASEP Exit Times. https://arxiv.org/abs/2310.08477

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