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作者：Radziwill, Maksym; Soundararajan, K.
作者单位：Institute for Advanced Study - USA; Stanford University
摘要：We show that if one can compute a little more than a particular moment for some family of L-functions, then one has upper bounds of the conjectured order of magnitude for all smaller (positive, real) moments and a one-sided central limit theorem holds. We illustrate our method for the family of quadratic twists of an elliptic curve, obtaining sharp upper bounds for all moments below the first. We also establish a one sided central limit theorem supporting a conjecture of Keating and Snaith. Ou...
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作者：Gloria, A.; Neukamm, S.; Otto, F.
作者单位：Universite Libre de Bruxelles; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Max Planck Society
摘要：We study quantitatively the effective large-scale behavior of discrete elliptic equations on the lattice with random coefficients. The theory of stochastic homogenization relates the random, stationary, and ergodic field of coefficients with a deterministic matrix of effective coefficients. This is done via the corrector problem, which can be viewed as a highly degenerate elliptic equation on the infinite-dimensional space of admissible coefficient fields. In this contribution we develop new q...
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作者：Miclo, Laurent
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Consider an ergodic Markov operator M reversible with respect to a probability measure mu on a general measurable space. It is shown that if M is bounded from L-2(mu) to L-p(mu), where p > 2, then it admits a spectral gap. This result answers positively a conjecture raised by Hoegh-Krohn and Simon (J. Funct. Anal. 9:121-80, 1972) in the more restricted semi-group context. The proof is based on isoperimetric considerations and especially on Cheeger inequalities of higher order forweighted finit...
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作者：Hryniewicz, Umberto; Momin, Al; Salomao, Pedro A. S.
作者单位：Universidade Federal do Rio de Janeiro; Universidade de Sao Paulo
摘要：We consider Reeb flows on the tight 3-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link. This result admits a natural comparison to the Poincar,-Birkhoff theorem on area-preserving annulus homeomorphisms. An analogous theorem...
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作者：Frantzikinakis, Nikos
作者单位：University of Crete
摘要：We study the structure of multiple correlation sequences defined by measure preserving actions of commuting transformations. When the iterates of the transformations are integer polynomials we prove that any such correlation sequence is the sum of a nilsequence and an error term that is small in uniform density; this was previously known only for measure preserving actions of a single transformation. We then use this decomposition result to give convergence criteria for multiple ergodic averag...
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作者：Melbourne, Ian; Terhesiu, Dalia
作者单位：University of Warwick; University of Vienna
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作者：Manners, Freddie
作者单位：University of Oxford
摘要：The pyjama stripe is the subset of consisting of a vertical strip of width around every integer -coordinate. The pyjama problem asks whether finitely many rotations of the pyjama stripe around the origin can cover the plane. The purpose of this paper is to answer this question in the affirmative, for all positive . The problem is reduced to a statement closely related to Furstenberg's Theorem from topological dynamics, and is proved by analogy with that result.
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作者：Baladi, Viviane; Benedicks, Michael; Schnellmann, Daniel
作者单位：University of Copenhagen; Royal Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider families of nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure of , as a function of on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming existence of a transversal CE parameter, we find a positive measure set of CE parameters , and, for each , a set of polynomially recurrent parameters containing as a Lebesgue density point, and constants , , so that, for every -Holder function , In addition, for all , the renormalis...
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作者：Lev, Nir; Olevskii, Alexander
作者单位：Bar Ilan University; Tel Aviv University
摘要：We characterize the measures on which have both their support and spectrum uniformly discrete. A similar result is obtained in for positive measures.
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作者：Kozma, Gady; Nitzan, Shahaf
作者单位：Weizmann Institute of Science; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent
摘要：We show that any finite union of intervals supports a Riesz basis of exponentials.
