On Bernoulli decomposition of random variables and recent various applications
Séminaire Équations aux dérivées partielles (Polytechnique) (2007-2008), Talk no. 9, 12 p.

In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.

@article{SEDP_2007-2008____A9_0,
     author = {Germinet, Fran\c cois},
     title = {On Bernoulli decomposition of random variables and recent various applications},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2007-2008},
     note = {talk:9},
     mrnumber = {2532944},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2007-2008____A9_0}
}
Germinet, François. On Bernoulli decomposition of random variables and recent various applications. Séminaire Équations aux dérivées partielles (Polytechnique) (2007-2008), Talk no. 9, 12 p. http://www.numdam.org/item/SEDP_2007-2008____A9_0/

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