11 Result(s)
within
Scott Sheffield
Mathematical and Computational Biology
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Article
Sums of GUE matrices and concentration of hives from correlation decay of eigengaps
Associated to two given sequences of eigenvalues \(\lambda _1 \ge \cdots \ge \lambda _n\) ...
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Geodesics and metric ball boundaries in Liouville quantum gravity
Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter
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Open AccessNon-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces
We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble $$\hbox {CLE...
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Open AccessLiouville quantum gravity and the Brownian map III: the conformal structure is determined
Previous works in this series have shown that an instance of a \(\sqrt{8/3}\) ...
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Scaling limits of the Schelling model
The Schelling model of segregation, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous clusters of o...
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Open AccessImaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the wa...
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Open AccessImaginary geometry I: interacting SLEs
Fix constants \(\chi >0\) χ > ...
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Power law Pólya’s urn and fractional Brownian motion
We introduce a natural family of random walks \(S_n\) on
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A contour line of the continuum Gaussian free field
Consider an instance \(h\) of the Gaussian free field on a simply connected planar domain
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The covariant measure of SLE on the boundary
We construct a natural measure μ supported on the intersection of a chordal SLE(κ) curve γ with \({\mathbb{R}}\) , in the range...
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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 w...
