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Showing 1 to 5 of 5 for “"Gaussian multiplicative chaos"”.
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On Gaussian Multiplicative Chaos
Gaussian multiplicative chaos was first constructed in Kahane's seminal paper in 1985 in an attempt to provide a mathematical foundation for Kolmogorov-Obukhov-Mandelbrot theory of energy dissipation in developed turbulence. It has attracted a lot of attentions from the mathematics community in the …
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On Gaussian multiplicative chaos and conformal field theory
… (CFT). The main probabilistic objects are the Gaussian free field (GFF) and the random geometries associated to it. Especially, we are interested in Gaussian multiplicative chaos (GMC), Schramm-Loewner evolution (SLE) and Liouville CFT, which can be understood as theories of random surfaces. …
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Scaling limit of critical systems in random geometry
… we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is …
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Thick points of random walk and multiplicative chaos
… unrelated area of Probability theory, called Gaussian multiplicative chaos. Firstly, in two dimensions, we answer a question of Dembo, Peres, Rosen and Zeitouni and compute the number of thick points of planar random walk, assuming that the increments are symmetric and have a finite moment of …
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Random conformally covariant metrics in the plane
… "$e^{\gamma h} (dx^2+dy^2)$'' where $h$ is a Gaussian free field (GFF) on a planar domain and $\gamma \in (0,2)$. Duplantier and Sheffield constructed the $\gamma$-LQG area and boundary length measures, which fall under the framework of Kahane's Gaussian multiplicative chaos. Later, a …