Surface fluctuations and their geometries.
Publication details: Rio de Janeiro: IMPA, 2013.Description: video onlineSubject(s): Online resources:
Partial contents:
We will first introduce in a heuristic way the natural generalization of Brownian motion to random surfaces i.e. heuristically speaking the random mountains defined in the continuum. We will discuss some basic features of this object called the Gaussian Free Field, such as its lack of continuity and we will discuss recent work that enable to describe its topography, focusing on the analogy with one-dimensional Brownian motion. This will be based on work by and joint work with Scott Sheffield, Jason Miller and Hao Wu
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We will first introduce in a heuristic way the natural generalization of Brownian motion to random surfaces i.e. heuristically speaking the random mountains defined in the continuum. We will discuss some basic features of this object called the Gaussian Free Field, such as its lack of continuity and we will discuss recent work that enable to describe its topography, focusing on the analogy with one-dimensional Brownian motion. This will be based on work by and joint work with Scott Sheffield, Jason Miller and Hao Wu
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