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引用次数: 0
摘要
本文给出了有限维向量空间中独立随机向量之和的反集中边界。特别是，我们渐近地建立了利德和拉德克里夫的猜想（SIAM J Discrete Math 7:90-101, 1994）和琼斯的问题（SIAM J Appl Math 34:1-6, 1978）。这项工作的亮点是 Chudnovsky 等人 (Ann Math 164:51-229, 2006) 在反集中背景下对强完美图定理的应用。
Anticoncentration of Random Vectors via the Strong Perfect Graph Theorem
In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (SIAM J Discrete Math 7:90–101, 1994) and a question of Jones (SIAM J Appl Math 34:1–6, 1978). The highlight of this work is an application of the strong perfect graph theorem by Chudnovsky et al. (Ann Math 164:51–229, 2006) in the context of anticoncentration.
期刊介绍：
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.
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