Bernoulli Trials of Fixed Parity, Random and Randomly Oriented Graphs

被引：0
作者：
Christos Pelekis
机构：
[1] KU Leuven,Informatics Section
来源：
Graphs and Combinatorics | 2016年 / 32卷
关键词：
Bernoulli trials; Randomly oriented graphs; Random graphs; Combinatorial probability; 60C05; 05C80;
D O I：
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中图分类号：
学科分类号：
摘要：
Suppose you can colour nbiased coins with n colours, all coins having the same bias. It is forbidden to colour both sides of a coin with the same colour, but all other colourings are allowed. Let X be the number of different colours after a toss of the coins. We present a method to obtain an upper bound on a median of X. Our method is based on the analysis of the probability distribution of the number of vertices with even in-degree in graphs whose edges are given random orientations. Our analysis applies to the distribution of the number of vertices with odd degree in random sub-graphs of fixed graphs. It turns out that there are parity restrictions on the random variables that are under consideration. Hence, in order to present our result, we introduce a class of Bernoulli random variables whose total number of successes is of fixed parity and are closely related to Poisson trials conditional on the event that their outcomes have fixed parity.
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页码：1521 / 1544
页数：23
相关论文
共 22 条
[1]  
Alavi Y(1987)The vertex independence sequence of a graph is not constrained Congr. Numer. 58 15-23
[2]  
Erdős P(2011)A counter-intuitive correlation in a random tournament Combin. Probab. Comput. 20 1-9
[3]  
Malde PJ(2012)Stochastic domination and weak convergence of conditioned Bernoulli random variables ALEA Lat. Am. J. Probab. Math. Stat. 9 403-434
[4]  
Schwenk AJ(1981)General percolation and random graphs Adv. Appl. Probab. 13 40-60
[5]  
Alm SE(2001)An orientation theorem with parity conditions Discrete Appl. Math. 115 37-47
[6]  
Linusson S(1995)The smallest uniform upper bound on the distance between the mean and the median of the Binomial and Poisson distributions Stat. Probab. Lett. 23 21-25
[7]  
Broman E(1956)On the Distribution of the Number of Successes in Independent Trials Ann. Math. Stat. 27 713-721
[8]  
van de Brug T(1980)Mean, median and mode in binomial distributions Stat. Neerl. 34 13-18
[9]  
Kager W(1991)Enumeration of digraphs with given number of vertices of odd out-degree and vertices of odd in-degree Discrete Math. 90 63-74
[10]  
Meester R(1993)On the number of successes in independent trials Stat. Sin. 3 295-312
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