{
  "id": "2407.21608",
  "version": "v1",
  "published": "2024-07-31T13:47:09.000Z",
  "updated": "2024-07-31T13:47:09.000Z",
  "title": "Integrability of the multi-species ASEP with long-range jumps on $\\mathbb{Z}$",
  "authors": [
    "Eunghyun Lee"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let us consider a two-sided multi-species stochastic particle model with finitely many particles on $\\mathbb{Z}$ defined as follows. Suppose that each particle is labelled by a positive integer $l$ and waits a random time exponentially distributed with rate $1$. It then chooses the right direction to jump with probability $p$ or the left direction with probability $q=1-p$. If the particle chooses the right direction, it jumps to the nearest site occupied by a particle $l'<l$ (with the convention that an empty site is considered as a particle with labelled $0$). If the particle chooses the left direction, it follows the rule of the multi-species totally asymmetric simple exclusion process (mTASEP). We show that this model is integrable and provide the exact formula of the transition probability using the Bethe ansatz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-31T13:47:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-range jumps",
      "multi-species asep",
      "left direction",
      "two-sided multi-species stochastic particle model",
      "integrability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}