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Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the m-th smallest point of ξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as k-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry. 相似文献
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Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E? to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this paper I set up a framework for studying the algebra of such functors, which I call formal plethories, in the case where E? is a Prüfer ring. I show that the “logarithmic” functors of primitives and indecomposables give linear approximations of formal plethories by bimonoids in the 2-monoidal category of bimodules over a ring. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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We consider the p -Zassenhaus filtration (Gn) of a profinite group G . Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in Sn. Under a cohomological assumption on the n-fold Massey products (which holds, e.g., if G has p -cohomological dimension ≤ 1), we prove that Gn+1 is the intersection of all kernels of upper-triangular unipotent (n+1)-dimensional representations of G over Fp. This extends earlier results by Miná?, Spira, and the author on the structure of absolute Galois groups of fields. 相似文献
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For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal(H)→BrPic(Rep(H)), from the group of equivalence classes of H -biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H=Tq is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(Tq)-bimodule categories. 相似文献
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Given n independent standard normal random variables, it is well known that their maxima Mn can be normalized such that their distribution converges to the Gumbel law. In a remarkable study, Hall proved that the Kolmogorov distance dn between the normalized Mn and its associated limit distribution is less than 3/log?n. In the present study, we propose a different set of norming constants that allow this upper bound to be decreased with dn≤C(m)/log?n for n≥m≥5. Furthermore, the function C(m) is computed explicitly, which satisfies C(m)≤1 and limm→∞?C(m)=1/3. As a consequence, some new and effective norming constants are provided using the asymptotic expansion of a Lambert W type function. 相似文献
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Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
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Consider in a real Hilbert space H the Cauchy problem (P0): u′(t)+Au(t)+Bu(t)=f(t), 0≤t≤T; u(0)=u0, where −A is the infinitesimal generator of a C0-semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem (P0) the following regularization (Pε): −εu″(t)+u′(t)+Au(t)+Bu(t)=f(t), 0≤t≤T; u(0)=u0, u′(T)=uT, where ε>0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem (Pε). Then we establish asymptotic expansions of order zero, and of order one, for the solution of (Pε). Problem (Pε) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C([0,T];H). However, the boundary layer of order one is not visible through the norm of L2(0,T;H). 相似文献
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For a space X denote by Cb(X) the Banach algebra of all continuous bounded scalar-valued functions on X and denote by C0(X) the set of all elements in Cb(X) which vanish at infinity. 相似文献
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The connected covering spaces of a connected and locally path-connected topological space X can be classified by the conjugacy classes of those subgroups of π1(X,x) which contain an open normal subgroup of π1(X,x), when endowed with the natural quotient topology of the compact-open topology on based loops. There are known examples of semicoverings (in the sense of Brazas) that correspond to open subgroups which do not contain an open normal subgroup. We present an example of a semicovering of the Hawaiian Earring H with corresponding open subgroup of π1(H) which does not contain any nontrivial normal subgroup of π1(H). 相似文献