Large deviations and concentration properties for ∇ϕ interface models

被引：0
作者：
Jean-Dominique Deuschel
Giambattista Giacomin
Dmitry Ioffe
机构：
[1] Fachbereich Mathematik,
[2] TU-Berlin,undefined
[3] Strasse des 17 Juni 136,undefined
[4] 10623 Berlin,undefined
[5] Germany. e-mail: deuschel@math.tu-berlin.de,undefined
[6] Dipartimento di Matematica,undefined
[7] Università di Milano,undefined
[8] via Saldini 50,undefined
[9] 20133 Milano,undefined
[10] Italy. e-mail: giacomin@mat.unimi.it,undefined
[11] Faculty of Industrial Engineering,undefined
[12] Technion,undefined
[13] Haifa 32000,undefined
[14] Israel. e-mail: ieioffe@ie.technion.ac.il,undefined
来源：
Probability Theory and Related Fields | 2000年 / 117卷
关键词：
Gradient Field; Gibbs Measure; Random Environment; Large Deviation Principle; Relaxation Property;
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摘要：
We consider the massless field with zero boundary conditions outside DN≡D∩ (ℤd/N) (N∈ℤ+), D a suitable subset of ℝd, i.e. the continuous spin Gibbs measure ℙN on ℝℤd/N with Hamiltonian given by H(ϕ) = ∑x,y:|x−y|=1V(ϕ(x) −ϕ(y)) and ϕ(x) = 0 for x∈DNC. The interaction V is taken to be strictly convex and with bounded second derivative. This is a standard effective model for a (d + 1)-dimensional interface: ϕ represents the height of the interface over the base DN. Due to the choice of scaling of the base, we scale the height with the same factor by setting ξN = ϕ/N.
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页码：49 / 111
页数：62
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