Convergence of the Two-Point Function of the Stationary TASEP

Jinho Baik (), Patrik Lino Ferrari () and Sandrine Péché ()
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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

A chapter in Singular Phenomena and Scaling in Mathematical Models, 2014, pp 91-110 from Springer

Abstract: 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.

Keywords: Height Function; Fredholm Determinant; Totally Asymmetric Simple Exclusion Process; Lebesgue Dominate Convergence Theorem; Asymmetric Simple Exclusion Process (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-00786-1_5

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DOI: 10.1007/978-3-319-00786-1_5

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