6期

最新文章

• MULTIVARIATE NORMAL APPROXIMATION FOR TRACES OF RANDOM UNITARY MATRICES AI翻译
  作者：Johansson, Kurt; Lambert, Gaultier
  作者单位：Royal Institute of Technology; University of Zurich
  摘要：In this article we obtain a superexponential rate of convergence in total variation between the traces of the first m powers of a n x n random unitary matrices and a 2m-dimensional Gaussian random variable. This generalizes previous results in the scalar case to the multivariate setting, and we also give the precise dependence on the dimensions m and n in the estimates with explicit constants. We are especially interested in the regime where m grows with n and our main result basically states ...
• MOMENTS OF THE RIEMANN ZETA FUNCTION ON SHORT INTERVALS OF THE CRITICAL LINE AI翻译
  作者：Arguin, Louis-Pierre; Ouimet, Frederic; Radziwill, Maksym
  作者单位：City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; California Institute of Technology
  摘要：We show that as T -> infinity, for all t is an element of [T, 2T] outside of a set of measure o(T), integral(log theta T)(-log theta T)vertical bar zeta(1/2 + it +ih)vertical bar(beta) dh = (log T)(f)((beta)+)(o(1))(theta), for some explicit exponent f(theta)(beta), where theta > -1 and beta > 0. This proves an extended version of a conjecture of Fyodorov and Keating (Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014) 20120503, 32). In particular, it shows that, for all theta...
• CONFORMAL GROWTH RATES AND SPECTRAL GEOMETRY ON DISTRIBUTIONAL LIMITS OF GRAPHS AI翻译
  作者：Lee, James R.
  作者单位：University of Washington; University of Washington Seattle
  摘要：For a unimodular random graph (G, rho), we consider deformations of its intrinsic path metric by a (random) weighting of its vertices. This leads to the notion of the conformal growth exponent of (G, rho), which is the best asymptotic degree of volume growth of balls that can be achieved by such a reweighting. Under moment conditions on the degree of the root, we show that the conformal growth exponent of a unimodular random graph bounds its almost sure spectral dimension. This has interesting...
• LIOUVILLE QUANTUM GRAVITY AND THE BROWNIAN MAP II: GEODESICS AND CONTINUITY OF THE EMBEDDING AI翻译
  作者：Miller, Jason; Sheffield, Scott
  作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
  摘要：We endow the root 8/3-Liouville quantum gravity sphere with a metric space structure and show that the resulting metric measure space agrees in law with the Brownian map. Recall that a Liouville quantum gravity sphere is a priori naturally parameterized by the Euclidean sphere S-2. Previous work in this series used quantum Loewner evolution (QLE) to construct a metric d(Q) on a countable dense subset of S-2. Here, we show that d(Q) a.s. extends uniquely and continuously to a metric (d) over ba...
• CONVERGENCE OF THE RANDOM ABELIAN SANDPILE AI翻译
  作者：Bou-Rabee, Ahmed
  作者单位：University of Chicago
  摘要：We prove that Abelian sandpiles with random initial states converge almost surely to unique scaling limits. The proof follows the Armstrong-Smart program for stochastic homogenization of uniformly elliptic equations. Using simple random walk estimates, we prove an analogous result for the divisible sandpile and identify its scaling limit as exactly that of the averaged divisible sandpile. As a corollary, this gives a new quantitative proof of known results on the stabilizability of Abelian san...
• ON THE REAL DAVIES' CONJECTURE AI翻译
  作者：Jain, Vishesh; Sah, Ashwin; Sawhney, Mehtaab
  作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
  摘要：We show that every matrix A is an element of R-n(xn) is, at least, delta parallel to A parallel to-close to a real matrix A + E is an element of R-nxn whose eigenvectors have condition number, at most, (O) over tilde (n)(delta(-1)). In fact, we prove that, with high probability, taking E to be a sufficiently small multiple of an i.i.d. real sub-Gaussian matrix of bounded density suffices. This essentially confirms a speculation of Davies and of Banks, Kulkarni, Mukherjee and Srivastava, who re...
• LIMITS OF SPARSE CONFIGURATION MODELS AND BEYOND: GRAPHEXES AND MULTIGRAPHEXES AI翻译
  作者：Borgs, Christian; Chayes, Jennifer T.; Dhara, Souvik; Sen, Subhabrata
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); Harvard University
  摘要：We investigate structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs et al. (Ann. Probab. 47 (2019) 2754-2800). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We introduce a notion of sampling convergence for sequences of multigraphs, and establish the graphex limit for the configuration model, a preferential attachment model, the generalized random graph and a bipartite variant o...
• ON STRONG SOLUTIONS OF ITO'S EQUATIONS WITH σ ∈ Wd1 AND b ∈ Ld AI翻译
  作者：Krylov, N., V
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W-d,loc(1) and the drift in L-d. We prove the unique strong solvability for any starting point and prove that, as a function of the starting point, the solutions are Holder continuous with any exponent < 1. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to...
• PERIODIC HOMOGENIZATION OF NONSYMMETRIC LEVY-TYPE PROCESSES AI翻译
  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-...
• SCALING LIMITS OF THE THREE-DIMENSIONAL UNIFORM SPANNING TREE AND ASSOCIATED RANDOM WALK AI翻译
  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...