-
作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H + x A with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched ...
-
作者：Gaudreau Lamarre, Pierre Yves; Lin, Yier; Tsai, Li-Cheng
作者单位：University of Chicago; Utah System of Higher Education; University of Utah
摘要：In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter root epsilon in front of the noise and let epsilon -> 0. We prove that the one-point large deviation rate function has a 3/2 power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the solution of the KPZ equation as epsilon -> 0. This confirms the physics prediction in Hartmann et al. (Phys Rev ...
-
作者：Dolgopyat, Dmitry; Hafouta, Yeor
作者单位：University System of Maryland; University of Maryland College Park; University System of Ohio; Ohio State University
摘要：We prove a Berry-Esseen theorem and Edgeworth expansions for partial sums of the form S-N = Sigma(N)(n=1) f(n)(X-n, Xn+1), where {X-n} is a uniformly elliptic inhomogeneous Markov chain and {f(n)} is a sequence of uniformly bounded functions. The Berry-Esseen theorem holds without additional assumptions, while expansions of order 1 hold when {f(n)} is irreducible, which is an optimal condition. For higher order expansions, we then focus on two situations. The first is when the essential suprem...
-
作者：Kim, Seonwoo
作者单位：Seoul National University (SNU)
-
作者：Inoue, Akihiko
作者单位：Hiroshima University
摘要：We derive novel explicit formulas for the inverses of truncated block Toeplitz matrices that correspond to a multivariate minimal stationary process. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the spectral density of the process. The derivation of the formulas is based on a recently developed finite prediction theory applied to the dual process of the stationary process. We illustrate the usefulness of the formulas by two applications. T...
-
作者：Arista, Jonas; Bisi, Elia; O'Connell, Neil
作者单位：University of Bielefeld; Technische Universitat Wien; University College Dublin
摘要：We study a discrete-time Markov process on triangular arrays of matrices of size d = 1, driven by inverse Wishart random matrices. The components of the right edge evolve as multiplicative random walks on positive definite matrices with one-sided interactions and can be viewed as a d-dimensional generalisation of log-gamma poly-mer partition functions. We establish intertwining relations to prove that, for suitable initial configurations of the triangular process, the bottom edge has an autono...
-
作者：Roeckner, Michael; Su, Yiming; Zhang, Deng
作者单位：University of Bielefeld; Zhejiang University of Technology; Shanghai Jiao Tong University
摘要：In this paper, we present a pathwise construction of multi-soliton solutions for focusing stochastic nonlinear Schrodinger equations with linear multiplicative noise, in both the L-2-critical and subcritical cases. The constructed multi-solitons behave asymptotically as a sum of K solitary waves, where K is any given finite number. Moreover, the con-vergence rate of the remainders can be of either exponential or polynomial type, which reflects the effects of the noise in the system on the asym...
-
作者：Dewan, Vivek; Muirhead, Stephen
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Melbourne
摘要：We prove upper bounds on the one-arm exponent eta(1) for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percolation of Gaussian fields, the arguments apply to other models in the Bernoulli percolation universality class, including Poisson-Voronoi and Poisson-Boolean percolation. More precisely, in dimension d = 2 we prove that eta(1) <= 1/3 for continuous Gaussian fields with rapid correlation decay (e.g. the Bargmann-Fock f...
-
作者：Lacoin, Hubert; Rhodes, Remi; Vargas, Vincent
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Aix-Marseille Universite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field X defined on a subset of R-d by the exponential of its cosine, namely exp (alpha integral cos(beta X)). It has gathered significant attention due to its importance in quantum field theory and to its connection with the study of log-gases in statistical mechanics. In spite of its relatively simple definition, the model has a very rich phenomenology. While the integral integral cos(beta X) can be defined prop...
-
作者：Ding, Jian; Song, Jian; Sun, Rongfeng
作者单位：Peking University; Shandong University; Shandong University; National University of Singapore
摘要：We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the external field is identically 0. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on Z(d), d >= 3...
