On the Chvatal-Janson conjecture

2021/04/24 by Lucio Barabesi, Lucio, Barabesi, Pratelli Luca +3
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2104.11971

openalex publication_date 2021/04/24 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper, Svante Janson has considered a conjecture suggested by Vašek Chv\a'atal dealing with the probability that a binomial random variable with parameters n and m/n - where m is an integer - exceeds its expectation m. Albeit Janson has provided a proof of this conjecture for large n, we show that the result actually holds for each n≥ 2.

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