{
  "id": "2209.10086",
  "version": "v1",
  "published": "2022-09-21T03:31:26.000Z",
  "updated": "2022-09-21T03:31:26.000Z",
  "title": "Spatial populations with seed-bank: finite-systems scheme",
  "authors": [
    "Andreas Greven",
    "Frank den Hollander"
  ],
  "comment": "56 pages, 7 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals carry type one of two types, live in colonies, and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. As geographic space labelling the colonies we consider a countable Abelian group endowed with the discrete topology. In earlier work we showed that the system has a one-parameter family of equilibria controlled by the relative density of the two types. Moreover, these equilibria exhibit a dichotomy of coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium). We identified the parameter regimes for which these two phases occur, and found that these regimes are different when the mean wake-up time of a dormant individual is finite or infinite. The goal of the present paper is to establish the finite-systems scheme, i.e., identify how a finite truncation of the system (both in the geographic space and in the seed-bank) behaves as both the time and the truncation level tend to infinity, properly tuned together. If the wake-up time has finite mean, then there is a single universality class for the scaling limit. On the other hand, if the wake-up time has infinite mean, then there are two universality classes depending on how fast the truncation level of the seed-bank grows compared to the truncation level of the geographic space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-21T03:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "60K35"
    ],
    "keywords": [
      "finite-systems scheme",
      "spatial populations",
      "geographic space",
      "equilibrium",
      "universality class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}