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Convergence of the Two-Point Function of the Stationary TASEP

In: Singular Phenomena and Scaling in Mathematical Models

Author

Listed:
  • Jinho Baik

    (University of Michigan, Department of Mathematics)

  • Patrik Lino Ferrari

    (Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Angewandte Mathematik)

  • Sandrine Péché

    (Université Paris Diderot, U.F.R. de Mathématiques)

Abstract

We consider the two-point function of the totally asymmetric simple exclusion process with stationary initial conditions. The two-point function can be expressed as the discrete Laplacian of the variance of the associated height function. The limit of the distribution function of the appropriately scaled height function was obtained previously by Ferrari and Spohn. In this paper we show that the convergence can be improved to the convergence of moments. This implies the convergence of the two-point function in a weak sense along the near-characteristic direction as time tends to infinity, thereby confirming the conjecture in the paper of Ferrari and Spohn.

Suggested Citation

  • Jinho Baik & Patrik Lino Ferrari & Sandrine Péché, 2014. "Convergence of the Two-Point Function of the Stationary TASEP," Springer Books, in: Michael Griebel (ed.), Singular Phenomena and Scaling in Mathematical Models, edition 127, pages 91-110, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00786-1_5
    DOI: 10.1007/978-3-319-00786-1_5
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