{
  "id": "1804.09571",
  "version": "v1",
  "published": "2018-04-25T13:51:34.000Z",
  "updated": "2018-04-25T13:51:34.000Z",
  "title": "The Intermediate Disorder Regime for Brownian Directed Polymers in Poisson Environment",
  "authors": [
    "Clément Cosco"
  ],
  "comment": "48 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime, which is a crossover regime between the strong and weak disorder regions. We show that, under a diffusive scaling involving different parameters of the system, the renormalized point-to-point partition function of the polymer converges in law to the solution of the stochastic heat equation with Gaussian multiplicative noise. The Poissonian environment provides a natural setting and strong tools, such as the Wiener-It\\^o chaos expansion, which, applied to the partition function, is the basic ingredient of the proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T13:51:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "82D60"
    ],
    "keywords": [
      "intermediate disorder regime",
      "brownian directed polymer",
      "poisson environment",
      "poissonian environment",
      "weak disorder regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}