32 citations · 81 across the 16 of their papers we have counts for
21 papers
Coupling Brownian loop soups and random walk loop soups at all polynomial scales
Wei Qian
Lawler and Trujillo Ferreras constructed a well-known coupling between the Brownian loop soups on and the (discrete-time) random walk loop soups on (o…
Parity questions in critical planar Brownian loop-soups (or "where did the free planar bosons go?")
Matthis Lehmkuehler, Wei Qian, Wendelin Werner
The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting Brownian loops in a planar domain that possesses some combinatorial features related to…
Conformally invariant fields out of Brownian loop soups
Antoine Jego, Titus Lupu, Wei Qian
Consider a Brownian loop soup with subcritical intensity in some 2D bounded simply connected domain. We define and study the properties of a confor…
Crossing exponent in the Brownian loop soup
Antoine Jego, Titus Lupu, Wei Qian
We study the clusters of loops in a Brownian loop soup in some bounded two-dimensional domain with subcritical intensity . We obtain an exact expression for the asymp…
Multiple points on the boundaries of Brownian loop-soup clusters
Yifan Gao, Xinyi Li, Wei Qian
For a Brownian loop soup with intensity in the unit disk, we show that almost surely, the set of simple (resp. double) points on any portion of boundary of any of its c…
A Geometric Approach to -means
Jiazhen Hong, Wei Qian, Yudong Chen +1
\kmeans clustering is a fundamental problem in many scientific and engineering domains. The optimization problem associated with \kmeans clustering is nonconvex, for which standard…
Conformal invariance of double random currents I: identification of the limit
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the converge…
Conformal invariance of double random currents II: tightness and properties in the discrete
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of lo…
Free boundary dimers: random walk representation and scaling limit
Nathanael Berestycki, Marcin Lis, Wei Qian
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched v…
Geodesics in the Brownian map: Strong confluence and geometric structure
Jason Miller, Wei Qian
We study geodesics in the Brownian map , the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our…
Structures of Spurious Local Minima in -means
Wei Qian, Yuqian Zhang, Yudong Chen
-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into clusters such that the within-cluster v…
Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities
Wei Qian, Yuqian Zhang, Yudong Chen
This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm…
Generalized disconnection exponents
Wei Qian
We introduce and compute the generalized disconnection exponents which depend on and another real parameter , extending the Brownian disconnection exponents…
The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
Jason Miller, Wei Qian
We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respe…
Conformal invariance of CLE on the Riemann sphere for
Ewain Gwynne, Jason Miller, Wei Qian
The conformal loop ensemble (CLE) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in and is indexed by a p…
Uniqueness of the welding problem for SLE and Liouville quantum gravity
Oliver McEnteggart, Jason Miller, Wei Qian
We give a simple set of geometric conditions on curves , in from to so that if is a homeomorphism whic…
The law of a point process of Brownian excursions in a domain is determined by the law of its trace
Wei Qian, Wendelin Werner
We show the result that is stated in the title of the paper, which has consequences about decomposition of Brownian loop-soup clusters in two dimensions.
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
Wei Qian, Wendelin Werner
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the sa…
Conditioning a Brownian loop-soup cluster on a portion of its boundary
Wei Qian
We show that if one conditions a cluster in a Brownian loop-soup (of any intensity) in a two-dimensional domain by a portion of its outer boundary, then in the remaining do…
Conformal restriction: The trichordal case
Wei Qian
The study of conformal restriction properties in two-dimensions has been initiated by Lawler, Schramm and Werner who focused on the natural and important chordal case: They charact…
Decomposition of Brownian loop-soup clusters
Wei Qian, Wendelin Werner
We study the structure of Brownian loop-soup clusters in two dimensions. Among other things, we obtain the following decomposition of the clusters with critical intensity: When one…