Construction of Gibbs measures for 1-dimensional continuum fields |
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Authors: | Yuu Hariya |
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Institution: | (1) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku Fukuoka, 812-8581, Japan |
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Abstract: | 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(ℝ;ℝ+) in terms of a certain rotationally invariant Gibbs measure on C(ℝ;ℝ3). |
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