Construction of Gibbs measures for 1-dimensional continuum fields

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We study 1-dimensional continuum fields of Ginzburg-Landau type under the presence of an external and a long-range pair interaction potentials. The corresponding Gibbs states are formulated as Gibbs measures relative to Brownian motion [17]. In this context we prove the existence of Gibbs measures for a wide class of potentials including a singular external potential as hard-wall ones, as well as a non-convex interaction. Our basic methods are: (i) to derive moment estimates via integration by parts; and (ii) in its finite-volume construction, to represent the hard-wall Gibbs measure on C(ℝℝ +) in terms of a certain rotationally invariant Gibbs measure on C(ℝℝ3).

Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalProbability Theory and Related Fields
Issue number1
Publication statusPublished - 2006 Sept


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