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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The level-set percolation of Gaussian free field
高斯自由场 水平 集渗流
2023/5/17
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： The level-set percolation of Gaussian free field
高斯自由场 水平集渗流 随机交错
2023/5/18
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Interlacement and Gaussian Free Field
交叠 高斯自由场 格林函数
2023/5/18
The (discrete) Gaussian free field (dGFF) on a transient graph, simply put, is the random Gaussian field with covariance given through Green’s function of the random walk on that graph. It is in many ...
In previous works, we showed that the internal DLA cluster on Zd with t particles is almost surely spherical up to a maximal error of O(log t) if d = 2 and O(√log t) if d ≥ 3. This paper addresses “av...
Extreme values for two-dimensional discrete Gaussian free field
Extreme values two-dimensional discrete Gaussian free field Probability
2012/6/15
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry...
Sharp asymptotics for Toeplitz determinants, fluctuations and the gaussian free field on a Riemann surface
Sharp asymptotics fluctuations the gaussian free Riemann surface
2011/7/26
Abstract: We consider canonical determinantal point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric and show that in the large N-limit t...
Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2
self-repelling random motion diffusion in random environment super-diffusivity
2011/2/28
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient...
Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field
recentered maximum two-dimensional discrete Gaussian Free Field
2010/12/8
We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long–standing conjecture. The proof c...