共查询到20条相似文献,搜索用时 15 毫秒
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Let denote the unit sphere in the Euclidean space . We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on . We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on . 相似文献
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A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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Ekaterina Vl. Bulinskaya 《Stochastic Processes and their Applications》2018,128(7):2325-2340
For a supercritical catalytic branching random walk on , , with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation. 相似文献
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Andrea Luigi Tironi 《Discrete Mathematics》2018,341(11):3152-3158
Let be a hypersurface in with defined over a finite field of elements. In this note, we classify, up to projective equivalence, hypersurfaces as above which reach two elementary upper bounds for the number of -points on which involve a Thas’ invariant. 相似文献
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An index , length quasi-cyclic code can be viewed as a cyclic code of length over the field via a basis of the extension . However, this cyclic code is only linear over , making it an additive cyclic code, or an -linear cyclic code, over the alphabet . This approach was recently used in Shi et al. (2017) [16] to study a class of quasi-cyclic codes, and more importantly in Shi et al. (2017) [17] to settle a long-standing question on the asymptotic performance of cyclic codes. Here, we answer one of the problems posed in these two articles, and characterize those quasi-cyclic codes which have -linear cyclic images under a basis of the extension . Our characterizations are based on the module structure of quasi-cyclic codes, as well as on their CRT decompositions into constituents. In the case of a polynomial basis, we characterize the constituents by using the theory of invariant subspaces of operators. We also observe that analogous results extend to the case of quasi-twisted codes. 相似文献
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Fatima Zahra Assila 《Comptes Rendus Mathematique》2018,356(3):283-287
We study the projective logarithmic potential of a probability measure μ on the complex projective space . We prove that the range of the operator is contained in the (local) domain of definition of the complex Monge–Ampère operator acting on the class of quasi-plurisubharmonic functions on with respect to the Fubini–Study metric. Moreover, when the measure μ has no atom, we show that the complex Monge–Ampère measure of its logarithmic potential is an absolutely continuous measure with respect to the Fubini–Study volume form on . 相似文献