Gaussian free fields for mathematicians
نویسندگان
چکیده
منابع مشابه
Gaussian free fields for mathematicians
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and som...
متن کاملMathematicians of Gaussian Elimination
G aussian elimination is universally known as “the” method for solving simultaneous linear equations. As Leonhard Euler remarked, it is the most natural way of proceeding (“der natürlichste Weg” [Euler, 1771, part 2, sec. 1, chap. 4, art. 45]). Because Gaussian elimination solves linear problems directly, it is an important technique in computational science and engineering, through which it ma...
متن کاملSome Discussions on Restrictions of Gaussian Free Fields and Massive Gaussian Free Fields
We are interested in two kinds of GFF. The rst one, mainly referred as GFF in the forth comings, is indexed by H(D), where D ⊆ R is some bounded domain, and H (D) is the closure of C∞ c (D) under the Dirichlet inner product (·, ·)∇ on D. The other one is the massive GFF. which is indexed by the standard Sobolev space H (R). As we can see from [3] and [4], when n = 2, the circle "average" of the...
متن کاملOn Generalized Gaussian Free Fields and Stochastic Homogenization
We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an “effective fluctuation tensor” that we denote by Q. We pro...
متن کاملGAUSSIAN FIELDS Notes for Lectures
DISCLAIMER: I have not (yet) properly acknowledged individually the sources for the material, especially in the beginning of the notes. These include Neveu’s and Adler’s courses on Gaussian processes [Ad90], the Ledoux-Talagrand book, and various articles. Acknowledgments: To the participants of the topics in probability (Fall 2013) at NYU for many comments, and to Nathanael Berestycki for addi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2007
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-006-0050-1