Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...
Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Let = { ∈ | () } be the language recognized by a formal series : → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.
Fábio Júlio Valentim (2012)
Annales de l'I.H.P. Probabilités et statistiques
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Fix a polynomial of the form () = + ∑2≤≤ =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑ ...
Francesco Ghiraldin (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy () −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....
Z. Masáková, T. Vávra (2014)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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We consider numeration systems with base and − , for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets Z and Z of numbers with integer expansion in base , resp. − . Our main result is the comparison of languages of infinite words and coding the ordering of distances between consecutive - and (− )-integers. It turns out that for a class of roots of − − , the languages coincide, while for other...
Marie Theret (2014)
ESAIM: Probability and Statistics
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We consider the standard first passage percolation model in ℤ for ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...
Marc Arnaudon, Laurent Miclo (2014)
ESAIM: Probability and Statistics
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Let be a complete Riemannian manifold, ∈ ℕ and ≥ 1. We prove that almost everywhere on = ( ,, ) ∈ for Lebesgue measure in , the measure μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...
Arturo Carpi, Aldo de Luca (2010)
RAIRO - Theoretical Informatics and Applications
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For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...
József Balogh, Béla Bollobás (2010)
RAIRO - Theoretical Informatics and Applications
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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...
Denis Belomestny (2010)
ESAIM: Probability and Statistics
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Let () be independent identically distributed bivariate vectors and , are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of and imply the same property for and , and under what conditions does the independence of and entail independence of and ? Some analytical sufficient conditions...
Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)
RAIRO - Theoretical Informatics and Applications
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We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When =1 we show that . In the cases when or max} we show that the first difference of the complexity function takes value in for every , and consequently we determine...
Sandrine Péché (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).
Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)
ESAIM: Probability and Statistics
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This paper deals with the problem of estimating the level sets () = {() ≥ }, with ∈ (0,1), of an unknown distribution function on ℝ . A plug-in approach is followed. That is, given a consistent estimator of , we estimate () by () = { () ≥ }. In our setting, non-compactness property is required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric...