Maxima in hypercubes
نویسندگان
چکیده
We derive a Berry-Esseen bound, essentially of the order of the square of the standard deviation, for the number of maxima in random samples from (0, 1)d. The bound is, although not optimal, the first of its kind for the number of maxima in dimensions higher than two. The proof uses Poisson processes and Stein’s method. We also propose a new method for computing the variance and derive an asymptotic expansion. The methods of proof we propose are of some generality and applicable to other regions such as d-dimensional simplex.
منابع مشابه
Explicit computation of the variance of the number of maxima in hypercubes
We present a combinatorial approach of the variance for the number of maxima in hypercubes. This leads to an explicit expression, in terms of Multiple Zeta Values, of the dominant term in the asymptotic expansion of this variance. Moreover, we get an algorithm to compute this expansion, and show that all coefficients occuring belong to the Qalgebra generated by Multiple Zeta Values, and by Eule...
متن کاملMaximal hypercubes in Fibonacci and Lucas cubes
The Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained 5 from Γn by removing vertices that start and end with 1. We characterize maximal induced hypercubes in Γn and Λn and deduce for any p ≤ n the number of maximal p-dimensional hypercubes in these graphs.
متن کاملCube intersection concepts in median graphs
In this paper, we study different classes of intersection graphs of maximal hypercubes of median graphs. For a median graph G and k ≥ 0, the intersection graph Qk(G) is defined as the graph whose vertices are maximal hypercubes (by inclusion) in G, and two vertices Hx and Hy in Qk(G) are adjacent whenever the intersection Hx ∩ Hy contains a subgraph isomorphic to Qk. Characterizations of clique...
متن کاملEmbedding Graphs with Bounded Treewidth into Optimal Hypercubes
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated. The dilation of the presented embedding is bounded by , where denotes the treewidth of the graph and denotes the maximal degree of a vertex in the graph. The given embeddi...
متن کاملVariance for the Number of Maxima in Hypercubes and Generalized Euler’s γ constants
In this work, we obtain some results à l’Abel dealing with noncommutative generating series of polylogarithms and multiple harmonic sums, by using techniques la Hopf. In particular, this enables to explicit generalized Euler constants associated to divergent polyzêtas. As application, we present a combinatorial approach of the variance for the number of maxima in hypercubes. This leads to an ex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 27 شماره
صفحات -
تاریخ انتشار 2005