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作者：Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
作者单位：Shanghai Jiao Tong University; University of Washington; University of Washington Seattle; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：In this paper we study homogenization problem for strong Markov processes on R-d having infinitesimal generators Lf(x) = integral(Rd) (f(x + z) - f(x) - (del f(x), z)1({vertical bar z vertical bar <= 1}))k(x, z)Pi(dz) +< b(x), del f(x)>, f is an element of C-b(2)(R-d) in periodic media, where Pi is a nonnegative measure on R-d that does not charge the origin 0, satisfies f(Rd) (1 <^> vertical bar z vertical bar(2))Pi(dz) < infinity and can be singular with respect to the Lebesgue measure on R-...
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作者：Angel, O.; Croydon, D. A.; Hernandez-Torres, S.; Shiraishi, D.
作者单位：University of British Columbia; Kyoto University; Technion Israel Institute of Technology; Technion Israel Institute of Technology; Kyoto University
摘要：We show that the law of the three-dimensional uniform spanning tree (UST) is tight under rescaling in a space whose elements are measured, rooted real trees, continuously embedded into Euclidean space. We also establish that the relevant laws actually converge along a particular scaling sequence. The techniques that we use to establish these results are further applied to obtain various properties of the intrinsic metric and measure of any limiting space, including showing that the Hausdorff d...
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作者：Salins, Michael; Spiliopoulos, Konstantinos
作者单位：Boston University
摘要：In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple asymptotically stable equilibria. When the system is exposed to small stochastic perturbations, it is likely to stay near one equilibrium for a long period of time but will eventually transition to the neighborhood of another equilibrium. We are interested in studyin...
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作者：Basu, Riddhipratim; Ganguly, Shirshendu; Hammond, Alan
作者单位：Tata Institute of Fundamental Research (TIFR); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：In last passage percolation models lying in the Kardar-Parisi-Zhang universality class, maximizing paths that travel over distances of order n accrue energy that fluctuates on scale n(1/3); and these paths deviate from the linear interpolation of their endpoints on scale n(2/3). These maximizing paths and their energies may be viewed via a coordinate system that respects these scalings. What emerges by doing so is a system indexed by x, y is an element of R and s, t is an element of R with s <...
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作者：Fan, Zhou; Mei, Song; Montanari, Andrea
作者单位：Yale University; University of California System; University of California Berkeley; Stanford University; Stanford University
摘要：We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as Z(2) synchronization. Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free e...
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作者：El Alaoui, Ahmed; Montanari, Andrea; Sellke, Mark
作者单位：Cornell University; Stanford University; Stanford University; Stanford University
摘要：Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper, we consider the case of Ising mixed p-spin models,; namely, Hamiltonians H-N : Sigma(N) -> R on the Hamming hypercube Sigma(N) = [+/- 1](N), which are defined by the property that {H-N(sigma)}(sigma is an element of Sigma N) is a centered Gaussian process with covariance E{H-N(sigma(1)) H-N(sigma(2))} depending only on the scalar product (sigma(1), sigma(2)). The as...
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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：Buraczewski, Dariusz; Iksanov, Alexander; Mallein, Bastien
作者单位：University of Wroclaw; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：We work under the Aidekon-Chen conditions which ensure that the derivative martingale in a supercritical branching random walk on the line converges almost surely to a nondegenerate nonnegative random variable that we denote by Z. It is shown that EZ 1({Z <= x}) = log x + o(log x) as x -> infinity. Also, we provide necessary and sufficient conditions under which EZ 1({Z <= x}) = log x + const + o(1) as x -> infinity. This more precise asymptotics is a key tool for proving distributional limit ...
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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...
