{
  "id": "1601.01937",
  "version": "v1",
  "published": "2016-01-08T16:46:06.000Z",
  "updated": "2016-01-08T16:46:06.000Z",
  "title": "Exponential convergence to the equilibrium for a class of 1D Lagrangian systems with random forcing",
  "authors": [
    "Alexandre Boritchev"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove exponential convergence to the stationary measure for a class of 1d Lagrangian systems with random forcing in the space-periodic setting: $\\phi_t+\\phi_x^2/2=F^{\\omega}, x \\in S^1 = \\mathbb{R}/\\mathbb{Z}$. Thus, we solve a conjecture formulated in \\cite{GIKP05}. Our result is a consequence (and the natural stochastic PDE counterpart) of the results obtained in \\cite{BK13, EKMS00}. It is also the natural analogue of the corresponding generic deterministic result \\cite{ISM09}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-08T16:46:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "1d lagrangian systems",
      "exponential convergence",
      "random forcing",
      "equilibrium",
      "natural stochastic pde counterpart"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101937B"
    }
  }
}