Abstract
First, we prove the following sharp upper bound for the number of high degree differences in bipartite graphs. Let be a bipartite graph with and . For we show that
Second, as a corollary, we confirm the Burdzy–Pitman conjecture about the maximal spread of coherent and independent vectors: for we prove that
for all random vectors satisfying and for some event A and independent σ-fields and .
Funding Statement
The work of the second-named author is supported by Junior Leader grant of Theoretical Physics and Mathematics Advancement Foundation “BASIS”.
Citation
Stanisław Cichomski. Fedor Petrov. "A combinatorial proof of the Burdzy–Pitman conjecture." Electron. Commun. Probab. 28 1 - 7, 2023. https://doi.org/10.1214/23-ECP512
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