伯兹-皮特曼猜想的一个组合证明

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-04-14 DOI:10.1214/23-ecp512

Stanisław Cichomski, F. Petrov

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引用次数: 6

摘要

我们证明了二部图中高阶差数的一个尖锐上界:设(U, V, E)是一个U = {U 1, U 2，…的二部图。， u n}和V = {v1, v2，…， v n};作为一个直接应用，我们给出了这个定理的一个稍微强一点的概率版本，从而证实了关于相干和独立分布的最大扩展的Burdzy-Pitman猜想。

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A combinatorial proof of the Burdzy–Pitman conjecture

We prove a sharp upper bound for the number of high degree differences in bipartite graphs: let ( U, V, E ) be a bipartite graph with U = { u 1 , u 2 , . . . , u n } and V = { v 1 , v 2 , . . . , v n } ; for n ≥ k > n 2 we show that As a direct application we show a slightly stronger, probabilistic version of this theorem and thus conﬁrm the Burdzy–Pitman conjecture about the maximal spread of coherent and independent distributions.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.