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A Proof of a Conjecture of Bobkov and Houdré

   
@article{ECP972,
	author = {S. Kwapien and M. Pycia and W. Schachermayer},
	title = {A Proof of a Conjecture of Bobkov and Houdré},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {1},
	year = {1996},
	keywords = {Gaussian distribution.},
	abstract = {S. G. Bobkov and C. Houdré recently posed the following question on the Internet  (Problem posed in Stochastic Analysis Digest no. 15 (9/15/1995)): Let $X,Y$ be symmetric i.i.d. random variables such that  $$P(|X+Y|/2 \geq t) \leq P(|X| \geq t),$$ for each $t>0$. Does it follow that $X$ has finite second moment (which then easily implies that $X$ is Gaussian)? In this note we give an affirmative answer to this problem and present a proof. Using a dierent method K. Oleszkiewicz has found another proof of this conjecture, as well as further related results.},
	pages = {no. 2, 7-10},
	issn = {1083-589X},
	doi = {10.1214/ECP.v1-972},    
        url = {http://ecp.ejpecp.org/article/view/972}}