共查询到20条相似文献,搜索用时 31 毫秒
1.
Jean‐Franois Delmas Jean‐Stphane Dhersin Marion Sciauveau 《Random Structures and Algorithms》2021,58(1):94-149
We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. This result is a first step for giving a nonparametric test for identifying the degree function of a large random graph. Replacing the indicator function in the empirical CDF by a smoother function, we get general asymptotic results for functionals of homomorphism densities for partially labeled graphs. This general setting allows to recover recent results on asymptotics for homomorphism densities of sampled graphon. 相似文献
2.
A. M. Sedletskii 《Mathematical Notes》2007,82(1-2):229-237
We find the asymptotics of the zeros of the degenerate hypergeometric function (the Kummer function) Φ(a, c; z) and indicate a method for numbering all of its zeros consistent with the asymptotics. This is done for the whole class of parameters a and c such that the set of zeros is infinite. As a corollary, we obtain the class of sine-type functions with unfamiliar asymptotics of their zeros. Also we prove a number of nonasymptotic properties of the zeros of the function Φ. 相似文献
3.
Ya. V. Kurylev 《Journal of Mathematical Sciences》1983,22(1):1082-1086
The Tauberian theorem of B. M. Levitan reduces the question of the asymptotics of the spectral function of the Laplace operator on a smooth Riemannian manifold with boundary to the problem of constructing the asymptotics of a Green function possessing certain additional properties. The paper is devoted to the construction of the appropriate Green function for the case of a geodesically concave boundary. 相似文献
4.
The spectral shift function of a Schrödinger operator with a perturbation of definite sign is considered. The asymptotics of the spectral shift function for large coupling constant is studied, and results concerning positive and negative perturbations are compared. A more general case of unperturbed operator given by a function of the Laplacian is discussed. This case explains the dependence of the asymptotics of the spectral shift function on the perturbation potential on the one hand and on the order of the unperturbed operator on the other hand. 相似文献
5.
A. S. Omuraliev 《Computational Mathematics and Mathematical Physics》2007,47(10):1675-1680
A regularized asymptotics of the solution to the time-dependent Schrödinger equation in which the spatial derivative is multiplied by a small Planck constant is constructed. It is shown that the asymptotics of the solution contains a rapidly oscillating boundary layer function. 相似文献
6.
Leonid Tolmatz 《Journal of Mathematical Analysis and Applications》2005,304(2):668-682
The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments. 相似文献
7.
Igor E. Pritsker 《Proceedings of the American Mathematical Society》1999,127(10):2953-2960
We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.
8.
A. A. Yakovlev 《Siberian Mathematical Journal》2010,51(2):370-382
We obtain the adiabatic asymptotics of the distribution function of the spectrum of the Laplace operator on a Riemannian Sol-manifold
with a one-dimensional invariant foliation. 相似文献
9.
D. S. Minenkov V. E. Nazaikinskii V. L. Chernyshev 《Functional Analysis and Its Applications》2016,50(4):291-307
We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. 相似文献
10.
Minoru Murata 《Journal of Differential Equations》2003,195(1):82-118
We give the asymptotics at infinity of a Green function for an elliptic equation with periodic coefficients on Rd. Basic ingredients in establishing the asymptotics are an integral representation of the Green function and the saddle point method. We also completely determine the Martin compactification of Rd with respect to an elliptic equation with periodic coefficients by using the exact asymptotics at infinity of the Green function. 相似文献
11.
《Journal of Applied Mathematics and Mechanics》2014,78(5):494-501
The field of internal gravity waves in a wedge-shaped region of a stratified medium is considered. Using a Kantorovich–Lebedev transformation, exact solutions are obtained which describe an individual mode and the complete wave field. The asymptotics of an individual wave mode are constructed by the WKB method, and are expressed in terms of a hypergeometric function, as well as the asymptotics of the complete wave field, which are expressed in terms of a semilogarithmic function. The results of numerical calculations of the wave field using the exact and asymptotic formulae are presented for the parameters of a stratified medium, characteristic for the dynamics of the ocean. The limits of their applicability are estimated. 相似文献
12.
N.M. Aslanova 《Siberian Mathematical Journal》2010,51(4):569-583
We study the asymptotics of the distribution function and compute the regularized trace of a boundary value problem for the
operator-differential equation with the boundary value depending on a spectral parameter. 相似文献
13.
讨论M/T-SPH/1排队平稳队长分布和平稳逗留时间分布的尾部衰减特征,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布。在分布PGF和LST的基础上,给出了两个平稳分布衰减规律的完整分析.结果表明,当参数取不同值时,平稳队长与平稳逗留时间的尾部具有三种不同类型的衰减特征. 相似文献
14.
Kh. K. Ishkin 《Differential Equations》2009,45(4):494-509
Using the Sturm-Liouville operator with a complex potential as an example, we analyze the spectral instability effect for operators that are far from being self-adjoint. We show that the addition of an arbitrarily small compactly supported function with an arbitrarily small support to the potential can substantially change the asymptotics of the spectrum. This fact justifies, in a sense, the necessity of well-known sufficient conditions for the potential under which the spectrum of the operator is localized around some ray. For an operator with a logarithmic growth, we construct a perturbation that preserves the asymptotics of the spectrum but has infinitely many poles inside the main sector. 相似文献
15.
S. I. Mitrokhin 《Russian Mathematics (Iz VUZ)》2018,62(6):27-42
We study a differential operator of the sixth order with an alternating weight function. The potential of the operator has a first-order discontinuity at some point of the segment, where the operator is being considered. The boundary conditions are separated. We study the asymptotics of solutions to the corresponding differential equations and the asymptotics of eigenvalues of the considered differential operator. 相似文献
16.
We find the asymptotics of the counting function of elements of an additive arithmetical semigroup for the case of an exponential counting function of prime generators, which has a natural interpretation in terms of Bose statistics as well as in the problem of counting the number of Gaussian packets on decorated graphs. 相似文献
17.
We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar metric. As an application, we determine the mean and almost-sure leading order behaviour of the high frequency asymptotics of the eigenvalue counting function associated with the natural Dirichlet form on the continuum random tree. We also obtain short time asymptotics for the trace of the heat semigroup and the annealed on-diagonal heat kernel associated with this Dirichlet form. 相似文献
18.
本文研究了连通分形鼓上的谱渐近,对满足“切口”条件的连通分形鼓以及一类自然连通的分形鼓,分别证明了弱Weyl-Berry猜想是成立的. 相似文献
19.
Spectral Asymtotic Behavior for a Class of Schrodinger Operators on 1-dimensional Fractal Domains
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In this paper, we study the spectral asymptotic behavior for a class of Schrödinger operators on 1-dimensional fractal domains. We have obtained, if the potential function is locally constant, the exact second term of the spectral asymptotics. In general, we give a sharp estimate for the second term of the spectral asymptotics. 相似文献
20.
M. A. Sokolov 《Journal of Mathematical Sciences》1983,23(4):2465-2470
Equations have been obtained, in a logarithmic approximation, for the infrared asymptotic behavior of a vertex function in a model of a massive isospinor field interacting with a massless isovector one. The particular solution obtained indicates the essential absence of infrared asymptotics of the vertex function in quantum electrodynamics. 相似文献