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作者：Peled, Ron; Spinka, Yinon
作者单位：Tel Aviv University; University of British Columbia
摘要：A proper q-coloring of a domain in Z(d) is a function assigning one of q colors to each vertex of the domain such that adjacent vertices are colored differently. Sampling a proper q-coloring uniformly at random, does the coloring typically exhibit long-range order? It has been known since the work of Dobrushin that no such ordering can arise when q is large compared with d. We prove here that long-range order does arise for each q when d is sufficiently high, and further characterize all perio...
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作者：Guralnick, Robert M.; Larsen, Michael; Tiep, Pham Huu
作者单位：University of Southern California; Indiana University System; Indiana University Bloomington; Rutgers University System; Rutgers University New Brunswick
摘要：The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to vertical bar G vertical bar in a logarithmic sense.
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作者：Kozlowski, Karol K.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：This paper develops a technique allowing one to prove the convergence of a class of series of multiple integrals which corresponds to the form factor expansion of space-like separated two-point functions in the 1+1 dimensional massive integrable Sinh-Gordon quantum field theory.
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作者：Berczi, Gergely; Kirwan, Frances
作者单位：Aarhus University; University of Oxford
摘要：The Green-Griffiths-Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang.
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作者：Fehrman, Benjamin; Gess, Benjamin
作者单位：University of Oxford; University of Bielefeld; Max Planck Society
摘要：Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate parabolic-hyperbolic PDE with irregular drift. We develop a robust well-posedness theory for such PDEs in energy critical spaces based on concepts of renormalized solutions and the equation's kinetic form. We establish these properties by proving that renormalized solutions a...
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作者：Sun, Song; Zhang, Junsheng
作者单位：University of California System; University of California Berkeley
摘要：We discover a no semistability at infinity phenomenon for complete Calabi-Yau metrics asymptotic to cones, which is proved by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kahler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
摘要：We study the frame properties of the Gabor systems G(g; alpha, beta) := {e(2 pi i beta mx) g(x - an)} m,n is an element of Z. In particular, we prove that forHerglotzwindows g such systems always form a frame for L-2(R) if alpha, beta > 0, alpha beta <= 1. For general rationalwindows g is an element of L-2(R) we prove that G(g; alpha, beta) is a frame for L-2(R) if 0 < alpha, beta, alpha beta < 1, alpha beta is not an element of Q and (g) over bar(xi) not equal 0, xi > 0, thus confirming Daube...
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作者：Skorobogatov, Alexei N.; Sofos, Efthymios
作者单位：Imperial College London; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; University of Glasgow
摘要：We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Chatelet equations.
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作者：Bessonov, R.; Denisov, S.
作者单位：Saint Petersburg State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; University of Wisconsin System; University of Wisconsin Madison
摘要：We give a dynamical characterization of measures on the real line with finite logarithmic integral. The general case is considered in the setting of evolution groups generated by de Branges canonical systems. Obtained results are applied to the Dirac operators and Krein strings.
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作者：Ford, Kevin; Ben Green; Koukoulopoulos, Dimitris
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Oxford; Universite de Montreal
摘要：We study the extent to which divisors of a typical integer n are concentrated. In particular, defining Delta(n) := max(t) #{d vertical bar n, log d is an element of [t, t + 1]}, we show that Delta(n) >= (log log n)(0.35332277...) for almost all n, a bound we believe to be sharp. This disproves a conjecture of Maier and Tenenbaum. We also prove analogs for the concentration of divisors of a random permutation and of a random polynomial over a finite field. Most of the paper is devoted to a stud...
