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作者：Chouk, Khalil; van Zuijlen, Willem
作者单位：University of Edinburgh; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0, L](2) with Dirichlet boundary conditions. We show that all of the eigenvalues divided by logL, converge as L -> infinity, almost surely to the same deterministic constant which is given by a variational formula.
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作者：Gwynne, Ewain; Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：We prove that the Tutte embeddings (a.k.a. harmonic/barycentric embeddings) of certain random planar maps converge to gamma-Liouville quantum gravity (gamma-LQG). Specifically, we treat mated-CRT maps, which are discretized matings of correlated continuum random trees, and gamma ranges from 0 to 2 as one varies the correlation parameter. We also show that the associated space-filling path on the embedded map converges to space-filling SLE kappa for kappa = 16/gamma(2) (in the annealed sense) a...
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作者：Ganguly, Shirshendu; Gheissari, Reza
作者单位：University of California System; University of California Berkeley
摘要：Consider the Ising model at low temperatures and positive external field lambda on an N x N box with Dobrushin boundary conditions that are plus on the north, east and west boundaries and minus on the south boundary. If lambda = 0, the interface separating the plus and minus phases is diffusive, having O(root N) height fluctuations, and the model is fully wetted. Under an order one field, the interface fluctuations are O(1), and the interface is only partially wetted, being pinned to its south...
