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On the convoy of the ASEP speed process
Yuan Tian · 2025-12-23 · via math.CO updates on arXiv.org

We investigate the size of the convoy in the speed process in the multi-species asymmetric simple exclusion process (ASEP). Through a coupling argument, we obtain an exact formula for the expected convoy size by relating it to a combinatorial structure. We prove that the asymptotic expected convoy size is universal for all fixed jump rates $q \in [0,1)$. In the special case $q=0$, we upgrade this to full convergence in distribution. We further establish a critical scaling $q = 1 - γ/\sqrt{n}$ that yields a nontrivial limiting regime. Our analysis builds on Martin's construction of the convoy and makes use of an orthogonal-polynomial representation of random-walk transition probabilities.