2017

最新文章

• Eigenvalues and entropy of a Hitchin representation AI翻译
  作者：Potrie, Rafael; Sambarino, Andres
  作者单位：Universidad de la Republica, Uruguay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
  摘要：We show that the critical exponent of a representation rho in the Hitchin component of PSL(d,R) is bounded above, the least upper bound being attained only in the Fuchsian locus. This provides a rigid inequality for the area of a minimal surface on rho\X where X is the symmetric space of PSL(d,R) The proof relies in a construction useful to prove a regularity statement: if the Frenet equivariant curve of rho is smooth, then rho is Fuchsian.
• The Sineβ operator AI翻译
  作者：Valko, Benedek; Virag, Balint
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
  摘要：We show that , the bulk limit of the Gaussian -ensembles is the spectrum of a self-adjoint random differential operator where is the positive definite matrix representation of hyperbolic Brownian motion with variance in logarithmic time. The result connects the Montgomery-Dyson conjecture about the process and the non-trivial zeros of the Riemann zeta function, the Hilbert-Plya conjecture and de Brange's attempt to prove the Riemann hypothesis. We identify the Brownian carousel as the Sturm-Li...
• Isometric disks are holomorphic AI翻译
  作者：Antonakoudis, Stergios M.
  作者单位：University of Cambridge
  摘要：This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmuller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichmuller disk. Additionally, a similar result is proved for a large class of disk-rigid domains, which includes strictly convex domains, as well as finite-dimensional Teichmuller spaces.
• The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error AI翻译
  作者：Pulvirenti, M.; Simonella, S.
  作者单位：Sapienza University Rome; University of L'Aquila; Technical University of Munich
  摘要：We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions, the correlation errors, measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order k measures the event where k particles are connected by a chain of interactions preventing the factorization. We show that, provided , such an error flows to...
• The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result AI翻译
  作者：Das, Tushar; Simmons, David
  作者单位：University of Wisconsin System; University of Wisconsin La Crosse; University of York - UK
  摘要：We construct a self-affine sponge in R-3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem tha...
• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature AI翻译
  作者：Marques, Fernando C.; Neves, Andre
  作者单位：Princeton University; Imperial College London
  摘要：In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifold with positive Ricci curvature and dimension at most seven contains infinitely many smooth, closed, embedded minimal hypersurfaces. In the last section we mention some open pro...
• Large deviation principle for empirical fields of Log and Riesz gases AI翻译
  作者：Leble, Thomas; Serfaty, Sylvia
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Institut Universitaire de France; New York University
  摘要：We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which ar...
• Minimal hypersurfaces with bounded index AI翻译
  作者：Chodosh, Otis; Ketover, Daniel; Maximo, Davi
  作者单位：University of Cambridge; Princeton University; Stanford University; University of Pennsylvania
  摘要：We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M-n, g), 3 <= n <= 7 can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems...
• The circular unitary ensemble and the Riemann zeta function: the microscopic landscape and a new approach to ratios AI翻译
  作者：Chhaibi, Reda; Najnudel, Joseph; Nikeghbali, Ashkan
  摘要：We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. Our scaling is performed at the so-called microscopic level, that is we consider the characteristic polynomial at points whose distance to 1 has order 1 / n. We prove that the rescaled characteristic polynomial does not even have a moment of order one, henc...
• On quasi-conformal (in-) compatibility of satellite copies of the Mandelbrot set: I AI翻译
  作者：Lomonaco, Luna; Petersen, Carsten Lunde
  作者单位：Universidade de Sao Paulo; Roskilde University
  摘要：Douady and Hubbard (Ann Sci Ec Norm Suppl 4 18(2):287-343, 1985) introduced the notion of polynomial-like maps. They used it to identify homeomorphic copies of the Mandelbrot set inside the Mandelbrot set . These copies can be primitive (with a root cusp) or satellite (without a root cusp). They conjectured that the primitive copies are quasiconformally homeomorphic to , and that the satellite ones are quasiconformally homeomorphic to outside any small neighbourhood of the root. These conjectu...