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;

D O I：

暂无

中图分类号：

学科分类号：

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.

引用

页码：49 / 111

页数：62